They went ahead on the half-hour mark when Tommy Doherty lost possession in midfield and Wycombe countered quickly by playing the ball through to Matt McClure to roll the ball under Artur Krysiak from 12 yards.
Exeter did not muster a shot at goal until the 40th minute when Alan Gow's shot was tipped over the bar by Matt Ingham, and they were little better in the second half.
Liam Sercombe's free-kick, easily pushed behind by Ingham, was as close as they came and it was no great surprise when Wycombe completed their win eight minutes from time.
Antony Stewart rose highest at the back post to head emphatically into the net from Matt Bloomfield's cross.
That goal failed to spark any sort of fightback from the Grecians, who have not won a cup game under manager Paul Tisdale since August 9, 2011.