Pools are now eight points short of safety after clinching only their second home victory of the season - their first since September.
Goals from Peter Hartley and James Poole earned the points as John Hughes' side won back-to-back games for the first time since September 2011.
County levelled when the lively Jamal Campbell-Ryce scored a fine individual effort in the 53rd minute, but despite being in the ascendancy County succumbed to Hartelpool's greater effort.
"I had a good feeling about this one," Hughes said. "It was so important to get that monkey off our back and get a first home win.
"There's 16 cup finals to come. We said in a team meeting that the best team doesn't always win and with a good nature and by being solid you can do that.
"Full credit to the boys, I'm delighted for them.
"We conceded a leveller and came back to win. This isn't going to be easy, but there's no point in shying away from it anymore.
"Let's go out with confidence. Other results don't bother me, all I'm interested in is Hartlepool and how we approach it."
He added: "Enjoy this win, and the feeling. Walk about with some pride from it. Let's inspire the supporters, we hounded the opposition and tackled for them."