The visitors had come to win by playing three up front, and it was their big striker Tes Bramble who caused the Bees most problems in the first half.
He gave veteran defender Paul Warhurst a torrid afternoon, and it was from one of Bramble's knockdowns that the visitors nearly broke the deadlock on 17 minutes. The ball dropped nicely for Adam Griffin on the left side of the box and he crashed a volley which Barnet stopper Ross Flitney did well to tip onto the inside of his near post.
Up to this point, Barnet had been the side trying to play the football, and it was a deft touch from striker Liam Hatch which put Dean Sinclair through on goal after just five minutes.
County keeper James Spencer did well to foil him but he was called into action again after Barnet changed their approach, their own big frontman Hatch was picked out in the box by a long ball on 32 minutes, and Spencer had to once again get down at Sinclair's feet after the knockdown.
Griffin had a great chance to put Stockport ahead on the stroke of half time but he put over from five yards, and was nearly left to rue the miss after the break.
Sinclair's chip to the far post on 50 minutes was met by the on rushing Nicky Bailey whose header forced a good save out of Spencer.
The keeper was then beaten by Hatch as he went through a minute later but the shot went inches wide.
This signaled the second half which Barnet were to dominate, although a clear cut chance was hard to come by.
Andy Hessenthaler was relentless in midfield but other than a few goal mouth scrambles from corners, Stockport weren't given a great deal to worry about.