The 2-0 win, which secured a home tie against League One Walsall at The 12th Imp Sincil Bank Stadium, was started in the 11th minute when the recalled Jake Sheridan met an Adam Smith cross before finishing neatly past Matt Glennon.
With City giving the hosts little time on the ball, they saw out a brief spell of Town pressure in the second half before putting the game beyond the reach of the Shaymen when Mamadou Fofana capitalised on some weak defending before squaring for Jamie Taylor who bagged his sixth of the season from six yards.
Substitute Colin Larkin rattled the woodwork as the Imps went for a third but the 2-0 success was more than sufficient to secure a place in the next round and £12,500 into the Club's coffers.
There were four changes to the City starting line-up for this FA Cup with Budweiser Fourth Qualifying Round Replay against FC Halifax Town at The Shay Stadium.
Replacing the injured Peter Gilbert was John Nutter, as he did in the 0-0 draw on Saturday whilst Mamadou Fofana came in for Dan Gray, Jake Sheridan was in for Nicky Nicolau and Alan Power returned in place of Conner Robinson in a role just behind Jamie Taylor. Vadaine Oliver was back in the fold and amongst the substitutes.
The home side kicked off and, as was the case at the weekend, it was a cagey opening to proceedings, although Halifax carved out the first half-chance with a Ryan Toulson cross being headed well wide by Lee Gregory in the sixth minute.
Toulson was in the action at the oher end four minutes later when he flicked away a Power effort from a narrow angle from within the six-yard box but it wasn't long before the Imps were pushing forward again and in the 11th minute they drew first blood when, after Adam Smith got past his marker on the right, he whipped in a centre and there to meet it was Jake Sheridan who finished neatly past Matt Glennon.
Whilst the celebrations were going on, Peter Bore limped off and a good couple of minutes had elapsed before he was replaced by Paul Robson at right-back.
City continued to push the Shaymen on the back foot as they pressed for a second with Smith and goalscorer Sheridan both looking threatening down the flankss whilst constant pressure from midfield ensured the home defence were given no time on the ball.
Saying that, it took good covering from Nutter to deny Gregory a sight of goal as the half entered its second quarter. Smith then required treatment after hitting the floor hard following an aerial challenge.
Halifax striker Gareth Seddon was then left on the turf after pulling up as he chased down Andrew Boyce. The experienced campaigner looked to be in some discomfort as he was helped to the touchline but miraculously returned with a spring in his step a minute later.
In the 36th minute the home side won the first corner of the evening and when the ball was pumped into the mix, a scuffle ensued before referee Seb Stockbridge had words with Smith and McManus. This chat took a good two minutes to take place before the official restarted things.
Town's next foray forward ended with Worsley having a shot blocked by Miller whilst in the run-up to three added minutes, City had the ball in the attacking third with Taylor flagged offside as he tried to latch on to a Mills chip over the top.
HT: Halifax 0 Imps 1
City were quickly out of the traps at the start of the second half with Taylor winning a corner on the right but Boyce stooped at the near post before heading Mills' flag-kick wide.
The Imps remained on the offensive with Glennon claiming a Nutter cross but had Paul Farman to thank in the 52nd minute as he palmed a Jon Worthington snap-shot behind. City dealt with the corner though and broke through Sheridan who saw his squared pass to Fofana hacked away by a Town defender.
A deflected Seddon shot then led to a Halifax corner but before this was taken Colin Larkin came on for Adam Smith for the Imps. Larkin was straight in the action, heading the flag-kick away to safety.
On the hour mark Taylor was booked for a clumsy foul on Bolland before a mazy run from Larkin saw him cut in from the right before seeing his low cross to Taylor intercepted by a blue shirted player.
Alan Power joined Taylor in the book for a challenge from behind on Hogan and from the resultant free-kick the hosts won their fifth corner of the game. After City dealt with this danger, Larkin broke before winning the Imps' second flag-kick which was claimed by Glennon at the second attempt.
The hosts' first change came in the 70th minute with Jason St Juste coming on for Scott McManus whilst a couple of minutes later a dipping effort from Power went just over Glennon's bar.
With a quarter of an hour remaining a surging run forward from Sheridan ended with Glennon tipping his goalbound effort behind for a corner which was hurriedly cleared. It wasn't long, though, before the Imps were on the attack again and when Fofana made the most of a slip in the home defence, he looked up and picked out Taylor who, after getting the ball under control, fired into the net with Glennon stranded.
With the tarvelling Imps on their feet in celebration, two nearly became three a minute later when Larkin cut in from the right before rattling the foot of the post with a left-foot shot. Goalscorer Taylor was then replaced by Vadaine Oliver for the remaining 10 minutes.
Halifax, looking to get back into the game, saw Farman claim a Worsley shot with ease as the clock ticked down. Worsley was then spoken to by the referee after he appeared to flick his head towards Miller prior to a Town corner.
A the other end Oliver appeared to be held back by Bolland but Mr Stockbridge spotted nothing untoward. City were then quick to close Halifax down in a bid to see time out. This was helped when Oliver won a corner after he was denied a shot at goal by Lowe.
The 100+ traveling City fans were quickly on their feet shortly afterwards when referee Stockbridge brought the game to a close with the professional effort from the Imps seeing them safely through to a First Round Proper tie against League One Walsall at The 12th Imp Sincil Bank Stadium.
FT: Halifax 0 Imps 2
City: Paul Farman, Peter Bore, Andrew Boyce, Tom Miller, John Nutter, Gary Mills, Mamadou Fofana, Jake Sheridan, Adam Smith, Alan Power, Jamie Taylor.
subs: Paul Robson (for Bore 13), Vadaine Oliver (for Taylor 80), Dan Gray, Nicky Nicolau, Graham Hutchison, Colin Larkin (for Smith 57), Jake Turner.
goals: Sheridan (11), Taylor (76)
bookings: Taylor (60), Power (65)
Halifax: Matt Glennon, Ryan Toulson, Scott McManus, Liam Hogan, Phil Bolland, Danny Lowe, Chris Worsley, Paul Marshall, Jon Worthington, Lee Gregory, Gareth Seddon.
subs: Phil Senior, Jason St Juste (for McManus 70), Simon Hackney, Conor Qualter, Dan Gardner.
Referee: Seb Stockbridge
Assistants: Dave McNamara & James Mainwaring
Fourth Official: Martin Woods
Attendance: 1,418 (130 City supporters)