The away side ended a run of four straight defeats to boost their own play-off chances.
The game was billed as a must-win for City but they went down to goals either side of half time.
Hartlepool started better of the two sides and had Bradford pegged back.
They should have been in front after 15 minutes but Richie Humphreys screwed his shot wide after Paul Henderson had superbly saved from Eifion Williams.
Gradually though Bradford did get back into the game but never really threatened Jim Provett in the United goal.
The opening period was a cagey affair but just when it looked as though the teams would go in level at the break the game burst into life.
With just three minutes left in the half the away side took the lead. Hugh Robertson slid a quick free-kick to Joel Porter who picked out strike partner Williams and he headed home from just six yards out.
The goal sparked Bradford into life and they should have been level just one minute later.
Dean Windass invaded the Hartlepool defence and slid in a tantalising low cross to Andy Cooke but his side-footed effort was superbly saved by Provett at point blank range.
City were back on level terms 15 minutes after the restart. Owen Morrison played a short corner to Marc Bridge-Wilkinson who slipped it back to the City winger. He then floated in an inviting cross that was thundered home by Mark Bower.
Bridge-Wilkinson then nearly gave City the lead when he caught Hartlepool out with a classic counter attack but the on loan midfielder saw his curling shot drift agonisingly wide.
It was the Hartlepool fans who went home happy though. A long throw was inadvertently flicked on by City full-back Peter Atherton and Porter was on hand to nod home at the back post.
Despite a late shout for a penalty, Hartlepool held on for a priceless three points.