The Blues had to do it the hard way, coming back from a goal down after Matt Rhead thumped home a header in the opening five minutes after a poor start from the hosts.
But they were literally handed a way back into the game when Martin Riley stuck out an arm to deflect Paul Hayes' shot, and the striker dispatched the penalty himself to level the scores.
The winning goal came with a quarter of an hour remaining when Hayes turned provider for Peter Murphy to head home in front of a gleeful home terrace.
The return of Josh Scowen, coupled with the absence of Paris Cowan-Hall, prompted a tactical reshuffle from Gareth Ainsworth, who handed Aaron Holloway his first league start in a 4-3-3- formation alongside Paul Hayes and Sam Wood up front.
Mansfield, in a 3-5-2 formation, created the game’s first chance when Matt Rhead flicked on for Rakish Bingham to get his shot away, but the striker’s powerful drive was parried away by Ingram.
The hosts didn’t heed the warning and allowed Bingham even more time moments later, but his tame shot was deflected into the side netting by Ingram, prompting a corner from which the opening goal arrived.
A delivery towards the back stick was met by a towering header from Matt Rhead, who evaded any challenge to send a bullet into the top corner with fewer than five minutes on the clock.
The goal sprung Wycombe into action and they caused panic for Stags keeper Dimitar Evtimov when he fumbled a long free-kick but Aaron Pierre was crowded out, before the defender fired over when the ball was returned into the box.
At the other end, Mansfield’s height caused a threat from set pieces and Rhead was gifted another free header on 14 minutes, but couldn’t aim it away from Ingram.
Half chances for Paul Hayes and Rakish Bingham evaded the target before the game involved into more of a midfield scrap, but the equalising goal came in controversial circumstances.
Paul Hayes fired speculatively goalwards from 25 yards and referee Darren Deadman deemed that Martin Riley had moved his arm towards the ball just inside the area, awarding a penalty which Hayes duly dispatched, despite the keeper’s best efforts.
Town looked shell-shocked and almost fell behind immediately when Hayes robbed a defender and escaped down the left, crossing the ball into the six-yard box only for Aaron Holloway to turn it over the bar when sliding in.
After a poor start, Wanderers finished the half strongly, and Holloway had a sight of a maiden Wycombe goal when Sam Wood’s cross missed everyone and flew past his boot at the back post as he just struggled to react in time.
Matt McClure replaced Holloway up front at the break and there seemed to be more tempo all over the park, as Mansfield continued to threaten from set-pieces into the penalty area.
One such opportunity saw Matt Rhead send another header towards goal and as Rakish Bingham looked set to turn the ball home, Sido Jombati hooked clear from within the six-yard box.
At the other end, Josh Scowen was relased after fine play from Sido Jombati and Sam Wood, but after some fine footwork, the ball was forced out for a corner.
Wanderers’ momentum was growing, and a brilliant passage of play almost let in Matt McClure, but his touch was just too heavy and it was scrambled clear.
Nevertheless, in the same movement, the ball was whipped in from the left and when Paul Hayes nodded it back across goal, Peter Murphy was in the right place at the right time to nod home his fourth goal of the campaign.
The midfielder sustained a head injury whilst scoring and needed to be replaced by Matt Bloomfield, and he was involved in a smart move in the final few minutes which resulted in Sam Wood's dipping volley being well saved by the keeper.
Stags boss Paul Cox was sent to the stands in stoppage time for an act of dissent, and it was the final act of note as the Blues held on for an impressive win.
Wycombe: Ingram, Jombati, Jacobson, Mawson, Pierre, Rowe, Murphy (Bloomfield 78), Scowen (Lewis 76), Wood, Holloway (McClure 45), Hayes.
Unused subs: Richardson, Walker, Kretzschmar.
Mansfield: Evtimov, Sutton, Tafazolli, Riley, Beevers (Taylor 85), Bell (Palmer 78), Murray, Marsden, Clements, Rhead, Bingham.
Unused subs: Studer, Fisher, McGuire, Heslop, Thomas.
Referee: Mr D Deadman
Attendance: 3,106 (261 from Mansfield Town)
Winning 50/50 Draw Number: 111254
Prize Money: £588.00