The Londoners were pegged back in their own half for most of a one-sided game, but broke out with seven minutes left for midfielder Barry Cogan to hammer a 25-yard shot into the top corner as the home defence backed off.
In a one-sided first half, on-loan Darryl Duffy thought he'd scored 11 minutes into his debut, but the Hull striker's header from a cross by Richie Humphreys was ruled out for offside.
The home side continued to dominate and, after defender Michael Nelson had missed the target with an unmarked header, Barnet keeper Lee Harrison almost gave away an own goal.
Jon Daly got in an angled shot that lacked power, but Harrison was taken by surprise and fumbled the ball into the air, relieved to see it bounce off the top of the bar and behind for a corner.
That was one of seven first-half corners for the home team, who also went close when Matty Robson crossed well from the left and Daly and Duffy both failed to connect in the middle.
A minute before the break, Gary Liddle's curling 25-yard free-kick was tipped over the bar by a busy Harrison.
Barnet's only first half threat came early on when Hartlepool produced a lot of good football, but let themselves down in the Barnet penalty area.
Nick Bailey got in a shot, but the power was taken off it by a deflection and home keeper Dimi Konstantopoulos saved comfortably.
It was just the same in the second half, David Foley having a goal disallowed for offside after he finished well with a low shot from the right of the area.
Nelson hit the Barnet bar with a header from a corner, and keeper Harrison made more good saves as the home pressure mounted.
Then with seven minutes left, Barnet broke out as their confidence grew and Cogan hammered a great 25-yard shot into the far top corner from the right of the area.