Stockport got themselves off to a dream start with a fine individual goal after just seven minutes.
Top scorer Liam Dickinson raced with the ball from inside his own half before slotting neatly past Frank Fielding from inside the box for his 20th goal of the season.
After a frantic start the pace dropped a little, until the 24th minute when Wycombe skipper Mike Williamson, straight from Delroy Facey's long throw-in, saw a header bounce out off the top of the Stockport crossbar.
Six minutes before the interval Stockport had a scare when Scott McGleish's close-range shot was only blocked by the backside of home skipper Gareth Owen.
McGleish ought to have done much better shortly before the break when smashing over wildly from 15 yards out.
Stockport keeper Conrad Logan was then forced to make a smart save to keep Tommy Doherty's shot out in first-half stoppage time.
McGleish got up well to head the first chance of the second half over the bar, while at the other end Dickinson fired straight into Fielding's grateful grasp.
Wycombe's Gary Holt fired in a header which was well-saved by Logan on the hour mark, before Facey headed over the bar from just eight yards.
However, somehow Stockport managed to hang on as they booked their date at Wembley.