Aston Villa scored seven second-half goals after trailing 3-1 at half-time.
Nathan Tyson, Roger Johnson and Tommy Mooney all scored headers for Wycombe, while a Steve Davis strike for Villa had at one point made the score 1-1.
Milan Baros's cool finish sparked the visitors' comeback, with a James Milner shot making it 3-3, while an own goal from Craig Easton put Villa ahead.
Gareth Barry then scored twice, his first with a penalty, with Milner and Davis also completing braces.
Wycombe manager John Gorman:
"We have embarrassed them into putting in a performance where they have embarrassed us. We made them play so well.
"The first half was no fluke. Everything we did was quality. And that fifth goal was not deserved.
"The referee gave them a penalty but he didn't book my player or send him off. Don't tell me that goal didn't matter. It was the goal that finished our team.
"It was a rubbish own goal and a deflected shot for the equaliser. They got the breaks. The scoreline was unjust in the end."
Aston Villa manager David O'Leary:
"We gave poor goals away and there were a few reminders at half-time, a few things to be said.
"In the end we ran out worthy winners and scored from good chances - I was very proud of them in the second half.
"It was very important that the second goal came early in the second half and it did.
"At half time it looked as though Wycombe were on the verge of a great victory without a doubt. We were on the verge of a cup shock if we didn't get our act together."
Wycombe: Talia, Senda, Williamson, Johnson, Easton, Burnell (Anya 84), Oakes, Bloomfield, Tyson (Torres 54), Mooney (Stonebridge 79), Dixon.
Subs Not Used: Williams, Martin.
Goals: Tyson 6, Johnson 18, Mooney 39.
Aston Villa: Sorensen, Samuel, Hughes (De la Cruz 83), Ridgewell, Cahill, Barry, Milner, Davis, Berger (Hendrie 79), Baros, Angel (Moore 68).Subs Not Used: Mellberg, Taylor.
Goals: Davis 14, Baros 48, Milner 64, Easton 69 og, Barry 73 pen, 78, Milner 86, Davis 90.
Ref: R Beeby (Northamptonshire).
The BBC is not responsible for the content of external internet sites