Adam Birchall scored twice as Barnet climbed to fifth in the table with their fourth successive victory.
Birchall swept home the opener from eight yards out from Jason Puncheon's left-wing cross but Anthony Elding levelled from the penalty spot.
Birchall restored Barnet's lead when he pounced on a loose ball and Josh Wright hit the third at the far post.
Ashley Carew erased any doubt about the result with the fourth before Liam Dickinson hit an injury-time reply.
Stockport: Logan, Briggs (Tansey 70), Owen, Williams, Tierney, Thompson, Taylor, Blizzard, Griffin (Proudlock 59), Elding (Dickinson 83), McNeil.
Subs Not Used: Jones, Turnbull.
Goals: Elding 25 pen, Dickinson 90.
Barnet: Harrison, Devera, Nicolau, Yakubu (O'Cearuill 18), Burton, Wright, Bishop, Carew, Puncheon, Norville (Hatch 74), Birchall.
Subs Not Used: Beckwith, Thomas, Porter.
Goals: Birchall 14, 47, Wright 62, Carew 84.
Att: 4,751
Ref: Mark Haywood (W Yorkshire).
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