Brighton striker Nicky Forster missed the first chance of the game when he blazed well wide after 12 minutes.
Seagulls defender Matt Richards then brilliantly thwarted the onrushing Davies before Stockport went in front after 33 minutes.
Anthony Pilkington's corner-kick wasn't cleared and Matty McNeil saw a shot blocked before the loose ball was fired home clinically by Blizzard from 15 yards.
Brighton came close to a leveller eight minutes into the second half when Forster turned smartly, only for his left-foot shot to strike the post.
Stockport then grabbed a second after 66 minutes when Brighton midfielder Bradley Johnson handled in the box, and on-loan striker Davies rammed home his third Stockport goal from the spot.