Lee Peacock struck twice in the second half to give City a comfortable passage into the Southern semi-final of the LDV Vans Trophy.
Scott Murray put the home side ahead in the 41st minute with his 17th goal of the season, a perfectly judged right-footed chip from 25 yards.
Peacock raced through a square defence to shoot low past Martin Taylor in the 64th minute and seven minutes later netted his second with a diving header from Aaron Brown's cross.
The home side totally dominated a match that was held up during the first half because referee Tony Leake had to go off with a hamstring injury.
Wycombe's best chance fell to Craig Faulconbridge, who shot wide from eight yards in the 52nd minute.