The game came to life in the closing stages of the opening period when skipper Gary Mills was upended in the area by Andy Pearson; Colin Larkin - starting in place of Jamie Taylor - did the honours from the spot for his first City goal.
Three goal in six second half minutes saw the entertainment continue as, after ex-Imp Scott Spencer had levelled from a penalty, Larkin repeated his first half feat after Mills was barged over again at the other end.
Hyde rallied though with experienced striker Phil Jevons levelling with a low shot from the edge of the box but it was left to Oliver to cap off another excellent performance with the winner; the big striker getting on the end of a cross from substitute Conner Robinson.
Colin Larkin for Jamie Taylor was the only change for this Blue Square Bet Premier game against Hyde at The 12th Imp Sincil Bank Stadium.
Whilst Larkin partnered Vadaine Oliver up front, Taylor dropped to the bench where he was joined by new signing David Morgan, who completed his youth loan move from Nottingham Forest yesterday.
Bright sunshine greeted the players as they were led out of the tunnel by referee Seb Stockbridge and once the pre-match formalities were done and dusted things got underway with City kicking off.
Within seconds of the start Vadaine Oliver clattered into Matt Cassidy, who then upended Nicky Nicolau making it a free-kick apiece in the opening minute. Some good Imps' pressure then saw the ball in the attacking third with a long Dan Gray throw-in being headed into David Carnell's gloves by Graham Hutchison.
Skipper Gary Mills then volleyed over following good work by Nicky Nicolau down the left before Gray tried his luck with a low skidding effort after home debutant Mamadou Fofana did well in the middle third.
A stray pass from Mills then forced Andrew Boyce to drag ex-Imp Scott Spencer to the deck with the centre-back earning a ticking off from referee Stockbridge. Spencer then won the first corner, putting Boyce under pressure on the left of the box. The deep flag-kick sailed over a packed area though and out for a goal-kick.
Hyde's best move of the game came on the quarter-hour mark with some neat one-touch build-up play ending with Spencer firing well over whilst City's response saw Nicolau connect with a Larkin cross only to see his header curl a foot wide.
City's first corner came in the 24th minute but this ended up with Gray slicing wide whilst shortly afterwards visiting 'keeper Carnell flapped at a Jake Sheridan cross only for the ball to run away from Larkin at the far post.
At the other end Boyce was at full stretch to rob Alex Brown following a clever Spencer pass with City' response seeing Carnell tip a Larkin effort wide after the striker latched on to a long John Nutter ball. The resultant corner, taken by Nicolau, ended with Boyce seeing his downward header hit the foot of the post before the loose ball was hacked behind. Before this corner could be taken Carnell required treatment before getting back to his feet.
City's next attack saw Sheridan test Carnell with a low effort whilst seven minutes before the break Sheridan had his shirt pulled as he prepared to shoot but with referee Stockbridge not spotting the incident, Carnell was able to save the City man's shot at goal.
A couple of minutes later and two minutes before the break the referee got it right as when Mills was barged to the ground under an Andy Pearson challenge following an excellent Oliver knock-down, he had the easy task of awarding the Imps a penalty. Colin Larkin took the responsibility from 12 yards and duly blasted into the roof of the net for his first goal in City colours.
City, with a deserved lead, continued to press the Hyde defence back as the half wore on and into two added minutes before the half ended with the visitors hacking away a free-kick.
HT: Imps 1 Hyde 0
It was as you were as Hyde restarted proceedings and it was the Imps who were quickly on the attack with Mills having a shot charged down after the visiting defence failed to deal with a dangerous Sheridan centre.
Five minutes into the second half David Poole replaced Matt Cassidy for the game's first substitution. A couple of minutes later Oliver nodded a Nicolau cross over before needing treatment after taking a knock to the back of his head when he hit the deck.
With Oliver grounded, Adam Griffin replaced Kelvin Lomax at left-back for the visitors, and a good two minutes had elapsed before the City striker was able to get to his feet and return to the fray.
A sweeping City move then ended wth Mills winning a corner which ended up seeing Boyce crowded out at the far post whilst the Imps' first change of the game saw Peter Bore replace Jake Sheridan in the 62nd minute.
Bore hadn't had chance to get his boots dirty, however, as within the space of a minute a trip on Liam Tomsett in the City box saw referee Stockbridge award his second penalty of the game; former Imp Scott Spencer doing the honours from the spot, finishing neatly past Paul Farman.
City responded by going on the attack and when Mills got himself into the area, he was crudely pushed in the back by Brown. Penalty number three and goal number two for Larkin who calmly sent Carnell the wrong way.
Before the game restarted Phil Jevons was cautioned following an off-the-ball scuffle with Gray but the striker had the last laugh five minutes later when, after City failed to clear their lines with Gray and Bore getting in each other's way, the ball ran straight to Jevons who drilled past Farman from just inside the box.
A rare break in play following this three-goal burst saw Hyde keeper Carnell go to ground again holding his left arm and when play recommenced, the visitors forced two corners in quick succession as they pressed for the lead. Poole then had a shot charged down as the home crowd started to get twitchy.
With the game in its last 10 minutes Conner Robinson replaced two-goal Colin Larkin and he was quickly in the action, combining with Mills before the latter went down in the area for a third time only for referee Stockbridge to deem that the skipper had fouled his man before going to ground.
In the 85th minute David Morgan replaced Nicky Nicolau for his City debut and he was involved in the move which led to the Imps regaining the lead four minutes later. The teenager and Mamadou Fofana combined well to gain possession and when the ball was played forward to Robinson, he squared for Vadaine Oliver to slot home from six yards.
The Fourth Official indicated that a minimum of five minutes were to be added on and in the first of these Brizzell fired across Farman and out for a welcome goal-kick which ate some seconds up. As did a weak Griffin centre which sailed straight over the City bar shortly afterwards.
The game ended in the City attacking third with substitute Robinson earning a great reception after taking the ball forward. The crowd stayed on their feet as referee Stockbridge brought things to a close.
FT: Imps 3 Hyde 2
City: Paul Farman, Dan Gray, Andrew Boyce, Graham Hutchison, John Nutter, Gary Mills, Mamadou Fofana, Nicky Nicolau, Jake Sheridan, Colin Larkin, Vadaine Oliver.
subs: Jamie Taylor, Peter Bore (for Sheridan 62), David Morgan (for Nicolau 85), Conner Robinson (for Larkin 81), Jake Turner.
goals: Larkin (43 pen, 65 pen), Oliver (89)
Hyde: David Carnell, Josh Brizzell, Andy Pearson, Luke Ashworth, Kelvin Lomax, Liam Tomsett, Matt Cassidy, Alex Brown, Stefan Cox, Scott Spencer, Phil Jevons.
subs: Adam Griffin (for Lomax 54), David Poole (for Cassidy 50), Callum Byrne, Rob Williams, Ashley Frith
goals: Spencer (64 pen), Jevons (70)
bookings: Jevons (66)
Referee: Seb Stockbridge
Assistants: Graeme Fyvie & Graham Kinnear
Fourth Official: Dean Appleby
Attendance: 1,745 (59 visiting supporters)