Goals from Steve Robinson, Rowan Vine and Ahmet Brkovic completed a quite comfortable victory which still leaves Stockport rooted in the bottom two with Blackpool.
Struggling County, coming into this game on the back of just one win all season, received a timely boost before kick-off when club skipper Danny Griffin was passed fit and he took his place in the heart of a leaky defence after six months out.
The home side opened brightly, and just four minutes in Warren Feeney's close-range shot was blocked by Luton's Chris Coyne, with Rickie Lambert's follow-up shot being deflected just wide.
Mike Newell's table-toppers responded in typical fashion, however, with Vine seeing a neat shot well saved by home goalkeeper James Spencer just before Steve Howard planted a free header narrowly wide.
The division's top marksman Howard then had a goal ruled out for a push, but two goals in a minute from the visitors left Stockport stunned.
Firstly Steve Robinson was allowed time and space just outside the box before smashing home an angled drive, then Vine latched on to a long ball from deep, left Griffin trailing in his wake then coolly slotted the ball underneath the advancing Spencer.
A stunning blow for Stockport, but they did rally and on the stroke of half-time Lambert turned nicely before rifling a low drive a whisker wide of the post.
Luton were soon back on the offensive, and just nine minutes after the break Howard nodded the ball into Brkovic's path and he in turn looped a header into the far corner of Spencer's goal.
On a miserable day Stockport did at least grab a late consolation goal from Lambert – a spectacular curling free-kick from all of 25 yards.