The Magpies opened the scoring in the 16th minute when Shola Ameobi thumped a header towards goal from a Rob Milsom corner, with Shaun Brisley getting the finishing touch to bundle home.
Kevin Nolan's side then doubled their lead early in the second half thanks to great work from Matt Tootle to get a cross into the box, where the impressive Ryan Yates nodded home.
Barnet, however, launched a late comeback and halved the Simeon Akinola drove inside the far post with seven minutes remaining, but were able to see the game out to leapfrog the Grecians up to top spot.
Pride of Nottingham was at the match and took photos of the fans before, during and after the game.
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