A home tie against local rivals Mansfield Town await the Imps after two goals in extra-time by substitute Vadaine Oliver did the damage after the teams were deadlocked at one goal apiece for the second successive game.
City took the lead courtesy of an Alan Power strike after he sprung the Saddlers' offside trap and the Imps looked to be on their way to a 1-0 success only for Richard Taundry to level matters with nine minutes remaining.
Up stepped Vadaine Oliver. The young substitute, fresh from his goal at Barrow on Saturday, repeated the feat when he headed in a Power corner in the 102nd minute and with time ticking on, he added a second when he made the most of a weak James Chambers to prod past David Grof.
A last-gasp deflected Jamie Paterson free-kick proved only to be of consolation for the home side with the Imps fully deserving of the cup success; the travelling fans quick to salute the squad on becoming the first City team to defeat at team from two divisions higher in the competition.
City were unchanged for a fourth successive game as they faced League One Walsall in this FA Cup with Budweiser First Round Replay at The Banks's Stadium.
A 1-1 draw 10 days ago brought about this replay and the Imps went into the game in a confident mood having extended their unbeaten league and cup run to eight games at the weekend with a 2-1 win at Barrow. Amongst the substitutes was second year scholar Rob Taylor who was involved in the first team squad for the first time.
Backed by a noisy band of travelling fans, City kicked off and were quick to press forward with Walsall 'keeper David Grof dropping a long Dan Gray throw-in to concede the game's first corner but Gary Mills' ball ended up with Alan Power firing well over.
Walsall's response saw Febian Brandy felled by Peter Gilbert but the Imps' defence easily dealt with the resultant free-kick whilst at the other end Graf let a header back from his centre-half slip through his grasp for another corner which was hurriedly cleared by the home defence.
Power then fired over from 25 yards as the Imps continued to enjoy the better of the early exchanges, although a save from Paul Farman saw him keep out the first shot on goal which came from Malvind Benning.
Walsall's first spell of pressure ended up with Tom Miller conceding a free-kick as he left a foot in on the lively Brandy but Jamie Paterson's effort was straight at the City wall before good work from Mills saw him win a goal-kick.
A free-kick for the Imps in a decent position came about in the 19th minute and when Power floated in a deep centre, Andrew Boyce's header across the box was deflected out for what turned out to be an unproductive corner.
City had a let off midway through the half when, after Adam Smith conceded possession cheaply midway inside his own half, Paterson cut in from the right only to blaze his effort well wide of the target. Benning then fizzed a long-range effort well past the other upright from the Saddlers' next attack.
A collision between Power and James Chambers brought about a break in play as the half-hour mark approached but both players were able to resume their duties. Nicky Featherstone then went in late on Peter Gilbert for a City free-kick which was taken by Power and dropped by Grof before Boyce saw his follow-up effort deflect for a corner which ended up seeing Taylor flick a header wide.
A quiet spell followed although the Imps continued to hold their own against the team two divisions higher with a couple of long Gray throw-ins putting the home defence under pressure as the Fourth Official prepared to indicated that a minimum of two added minutes were to be played.
Midway through the extra stages Farman was forced to pounce on a deflected Brandy cross whilst the half ended with a Gray ball into the box being punched clear by Grof who claimed Smith's follow-up ball into the box.
HT: Walsall 0 Imps 0
Both sides emerged unchanged for the start of the second half and within a couple of minutes of the restart the Imps had Farman to thank as he came off his line quickly to deny Brandy after the Walsall man had got a sight of goal despite appearing to foul Gray. Shortly afterwards Brandy was at it again before firing into the side netting.
Citys response was immediate and, after Miller swept up to intercept a Walsall attack, his forward ball was spotted by Power who judged his run perfectly to spring the offside trap and, as Grof came out to narrow the angle, the Imps' number eight produced a fine finish to bring the 348 travelling fans to their feet behind the goal.
A couple of minutes later Sheridan won a corner and when Power's delivery was played back to him and then Gray, the latter's ball was fized over by Sheridan at full stretch 20 yards out. Walsall's response saw them force their first corner of the game but Taundry's deep delivery was unable to be kept in by skipper Butler.
A Mills free-kick led to a City corner but Power's delivery to the near post was cleared for a throw-in and as the Imps kept up the pressure a Smith ball into the mix saw Taylor penalised for a push as he stooped for a header.
What little Walsall were throwing at the Imps, the City defence were remaining sturdy as the game approached its final quarter, although a foul on Benning by Gray gave the hosts a free-kick close to the corner flag which resulted in a corner which Farman punched away.
In the 70th minute a crude late challenge on Smith earned Richard Taundry a deserved yellow card and before the free-kick could be taken Aaron Williams replaced George Bowerman for the home side.
When play restarted skipper Gary Mills picked up a booking for a foul close to the half-way line before Sheridan was denied a sight of goal after Grof sprinted off his line to clear following a forward ball down the flank.
Gray followed Mills into the book with 13 minutes remaining for a tug on Benning whist Ashley Hemmings for Febian Brandy was Walsall's second change two minutes later, must to the annoyance of the home fans.
With 10 minutes on the clock Vadaine Oliver replaced Adam Smith for City but within 60 seconds the home side gave themselves a fighting chance when, after the Imps failed to clear their lines, a ball towards the edge of the box found Taundry who drilled low past Farman for the leveller.
Shortly after the restart the hosts won a corner which was claimed by Farman who booted the ball out to give Gray the chance to receive treatment after he took a knock. Peter Bore came on as his replacement.
Taundry fired well wide following a quick Walsall counter-attack with 90 seconds remaining whilst four added minutes was indicated as the Imps won a couple of throw-ins on their right.
Midway through the added minutes Boyce was penalised for a push close to the touchline but Bore headed the free-kick clear. Bore then repeated Boyce but this free-kick was hacked away by Taylor.
The 90 minutes ended with Hemmings drilling wide so the teams faced at least an extra 30 minutes to decide the winner.
WALSALL 1 IMPS 1
The Saddlers got extra-time underway and within the first 30 seconds Adam Chambers fired a volley over after a ball into the box crashed against Boyce. At the other end Grof cleared from both Taylor and Oliver after the latter won a decent flick-on.
A City free-kick then ended with Grof claiming a Miller header whilst Walsall's response saw Paterson let fly from range but thankfully his effort flew well wide of the target.
Some excellent play between Power, Sheridan and the overlapping Bore brought about a City corner 12 minutes and this set-piece brought about a second goal for the Imps as, after Power floated the ball into the mix, there was Oliver to power a header into the corner of the net, just as he did at Barrow in the league on Saturday.
City saw out the remainder of the first half of extra-time before play restarted after a well-earned drink and a chat from the management team on the touchline for the Imps.
Walsall's Featherstone picked up a booking for dissent in the first minute following the latest restart after a hand-ball on the half-way line. A minute later a deflected Paterson effort led to a corner which was headed wide at the back post by Butler.
Sheridan was then forced to concede another corner as the hosts pressed forward again and when this was played back in James Chambers fired lamely into the side netting.
Both sides made a switch with nine minutes remaining; John Nutter for Alan Power for the Imps and Jake Jones for Richard Taundry for the home side.
Nutter's first touch saw him concede a corner which eventually saw the ball land in Farman's gloves; a couple of City throw-ins then saw them eat some seconds up before the hosts won a goal-kick.
At the other end Farman blocked a Williams shot following a game of pin-ball in the City area before the City stopper claimed a long-throw. He duly pumped the ball forward, James Chambers tamely headed back to Grof and in nipped Oliver to slide past the stranded 'keeper to give the Imps a two goal lead with three minutes remaining.
Oliver was booked before the restart for over celebrating his goal and the Imps had an additional couple of minutes to see out for a place in the second round.
A foul by Gilbert on Hemmings gave the hosts a chance from a free-kick in a dangerous position midway through the added stages
Paterson saw his effort take a wicked deflection with Farman unable to stop the ball from going over the line to make for a dramatic finale. There was still time for referee to add an extra two minutes but when Farman pumped forward a goal-kick, the game eventually came to a close with the Imps' fans on their feet to salute the record-breaking squad on becoming the first City team to defeat at team from two divisions higher in the FA Cup.
FT: Walsall 2 Imps 3 (AET)
City: Paul Farman, Dan Gray, Andrew Boyce, Tom Miller, Peter Gilbert, Gary Mills, Mamadou Fofana, Jake Sheridan, Adam Smith, Alan Power, Jamie Taylor.
subs: John Nutter (for Power 111), Vadaine Oliver (for Smith 80), Peter Bore (for Gray 85), Rob Taylor, Colin Larkin, Conner Robinson, Jake Turner.
goals: Power (50), Oliver (102, 117)
bookings: Mills (72), Gray (77), Oliver (118)
Walsall: David Grof, Richard Taundry, Andy Butler, Dean Holden, Nicky Featherstone, Adam Chambers, Jamie Paterson, Febian Brandy, George Bowerman, Malvind Benning, James Chambers.
subs: Ashley Hemmings (for Brandy 79), Jake Jones (for Taundry 111), Ben George, Aaron Williams (for Bowerman 71), Paul Downing, James Baxendale, James Walker.
goals: Taundry (81), Paterson (120+2)
bookings: Taundry (70), Featherstone (106)
Referee: Graham Scott
Assistants: Adrian Gillett & Ian Rathbone
Fourth Official: Danny Gratton
Attendance: 1,762 (348 City supporters)