An entertaining opening half saw both sides create chances, but it was the hosts who went in at the break in front.
After a quiet opening spell it was Brighton who carved out the first opening, but Nicky Forster blasted well wide.
Stockport responded when Anthony Pilkington played a brilliant pass to the onrushing Craig Davies, only for Matt Richards to rescue the Seagulls with a well-timed tackle.
Matty McNeil then just couldn't quite stretch to meet a Davies cross.
In-form Stockport deservedly went in front after 32 minutes. Pilkington's corner-kick wasn't cleared, McNeil saw a shot blocked, but the loose ball fell to Dominic Blizzard and he fired home neatly from 15 yards.
County ought to have doubled their lead a minute later, but Brighton keeper Michels Kuipers did well to thwart the dangerous Davies.
Brighton looked invigorated after the restart and they came mighty close to a leveller on 53 minutes.
Forster hit a left-foot shot which beat Owain fon Williams, but bounced back out off the post.
Wales Under-21s international fon Williams then denied Forster with an excellent save just past the hour mark.
It was Stockport who went two up on 65 minutes though. Bradley Johnson handled in the box and up stepped Davies, who rammed home his third Stockport goal since joining the club on loan from Oldham earlier this month.
Davies then headed an effort narrowly wide, before Brighton tried to respond when Forster fired just past the post with another decent shot from distance.