The Chairboys showed no signs of tiredness despite their heroic midweek win over Charlton, goals in either half from Kevin Betsy and Hatters old boy Jermaine Easter doing the damage.
Stockport will feel hard done by though, the away side had long spells of pressure but just couldn't get past keeper Jamie Young.
The game couldn't have started better for Wycombe from their first corner of the game, after just 90 seconds, Stockport failed to clear and Betsy blasted the ball home from a couple of yards out.
Stockport had a glorious chance to level soon after, with Young at full stretch to keep out a Tes Bramble header. They seemed certain to score from the rebound only for some heroic goal-line defending to keep them at bay.
This started a good spell of possession for the Hatters, as they knocked the ball around well looking for an opening.
It was Wycombe who had a glorious chance to double their lead though. After a Stephen O'Halloran cross James Spencer's punch only went as for as Stefan Oakes, who poked the ball to Tommy Mooney, whose close-range shot was just deflected wide.
Stockport continued to have a lot of the ball, but it was Wycombe who went close again, this time from Easter who blasted wide from 15 yards.
Despite this Stockport could have gone in all square at the break but Young denied them again, keeping out Anthony Pilkington's back-post header.
Stockport started the second half with real intent and enjoyed a sustained period of good pressure without really creating much.
Wycombe did well to contain them though and started to play a bit of keep-ball themselves and got their reward on the 63 minute. Easter raced on to a throughball and lobbed Spencer coolly.
Stockport came back at Wycombe and sub Liam Dickinson had a superb half-volley well saved by Young.
Wycombe defended resolutely after that scare and deservedly hung on for all three points.