Wycombe started brightly with Mooney setting up Russell Martin for an early chance but his shot was well blocked by Shane Duff. Mooney was in the thick of again soon after, driving the ball across the face of the goal for Will Antwi who couldn't divert it on target.
As the rain lashed down, Rob Lee was forced off the field after receiving a nasty cut to the face following a collision with Guinan on the half-hour, being replaced by Joe Burnell.
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 Duff's knockdown to fire into the bottom corner past Steve Williams.
In a more open start to the second half, Mooney saw a goalbound header diverted wide by Duff, before Cheltenham squandered two excellent chances to extend their lead with Guinan and Duff both putting free headers wide.
Jermaine Easter almost made an immediate impact after being introduced as a substitute, but he saw his shot on the turn flash inches wide.
Stefan Oakes also went close with a free-kick before Town doubled their lead on 75 minutes. A good move involving Grant McCann, Kayode Odejayi and Guinan finished with the latter firing an angled shot under Williams.
Wycombe piled on the pressure towards the end and finally pulled back a goal deep into added-on time.
Mooney pounced on a loose ball in the area to hammer a shot past Higgs.