Gary Jones struck after 22 minutes for the Cods at Lincoln following good work from Andy Parkinson and former Sheffield United midfielder Curtis Woodhouse.
The Town striker kept his cool to side foot the ball past Lincoln keeper Alan Marriott.
Lincoln came close to grabbing an injury-time equaliser when a last-ditch effort from former Huddersfield defender Nat Brown was cleared off the line by Woodhouse.
The rebound fell to central defender Gareth McAuley, whose shot came back off the bar.
Referee Lee Mason disallowed two Lincoln goals in four minutes, the first for pushing by Lincoln captain Jamie McCombe after his header beat keeper Steve Mildenhall.
A late strike from Tommy Mooney gave Wycombe hope of a second-leg comeback after Cheltenham looked to have control of their tie after goals in each half from John Finnigan and Steve Guinan.
The visitors had rarely threatened during an increasingly tense and scrappy first half before they took the lead three minutes before the interval.
Robins captain Finnigan reacted quickest to Shane Duff's knockdown to fire into the bottom corner past Steve Williams.
Town doubled their lead after 75 minutes. A good move involving Grant McCann, Kayode Odejayi and Guinan finished with the latter firing home with an angled shot.
Wycombe piled on the pressure towards the end and finally pulled back a goal deep into added-on time when Mooney pounced on a loose ball in the area to hammer a shot past Higgs.