Two goals from loan striker Glenn Murray proved enough for the Hatters, as Richard Walker's 83rd minute strike for Rovers proved to be just a consolation effort.
In driving rain, there was a cagey start despite the greasy Edgeley Park surface.
County striker Tes Bramble couldn't quite latch on to Michael Raynes header into the danger zone, while Rovers frontman Walker glanced a header well over from ten yards.
The visitors seemed to be coping better with the conditions by the midway point in the first half. Lewis Haldane tried a shot, but goalkeeper James Spencer saved comfortably.
At least Haldane was making his presence felt up front for Rovers, and just beyond the half-hour mark he again found space just outside the Stockport box, but fired a shot just over the crossbar.
County did manage a response though, and just two minutes later Keith Briggs was unfortunate when he slipped just as he fired in a low drive which fizzed just past the post.
Briggs was the next to try his luck for County as he powered in a header from all of 18 yards, but the ball flew wide.
The deadlock was finally broken six minutes before the break, and it was Murray who pounced for his second goal of the season.
Left-back Michael Rose played a hopeful ball forward, it flicked off James Hunt, and there was Murray who raced clear before coolly slotting home.
Walker had a great chance to level matters a minute later, but he fired a free shot over the bar following a dreadful clearance by Spencer.
After the break ex-Stockport man Aaron Lescott shot wide for Rovers, then on 51 minutes Walker was unlucky when his hooked shot from 12 yards struck the outside of a post.
However, it was the home side who doubled their lead on 53 minutes when Murray intercepted a poor backpass from Byron Anthony before firing home from an angle despite goalkeeper Stephen Phillips' attempt to block the shot.
Rovers substitute Rickie Lambert then entered the fray to make his debut against one of his former clubs and he almost made an immediate impact, but Spencer saved his close-range shot superbly.