Gavan Holohan was shown a second yellow card before substitute Paul McCallum gave the Bees the lead with his first touch on his debut.
A Dan Sweeney own goal levelled things up for Pools before Simeon Akinola sealed the three points for the hosts five minutes later.
Scroll down and click through the pages to see the Hartlepool player ratings from the match...
1. Mitchell Beeney - 4
Made a couple of decent stops but still unconvincing in coming for and claiming the ball. Possibly could have come off his line to remove the threat leading up to the second goal and was in no man's land for the first. Photo: Frank Reid
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2. Mark Kitching - 5
Another who had to recover and defend after being caught out of position on a few occasions. Often recovered well but was guilty of giving Barnet too much space to exploit in the final third. Photo: Frank Reid
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3. Timi Odusina - 5
Was fortunate not to give away a penalty in the first half and was booked following a rash challenge right on the edge of the box. Some good last ditch defending at times but struggled to read the movement of Barnet’s attack. Photo: Frank Reid
4. Gary Liddle - 6
Won some important headers and kept his composure despite a difficult afternoon at the back. Photo: Frank Reid