John Miles scored a rare double to get Stanley back to winning ways and boost their play-off charge.
Saturday's clash against the former Premier League club was massive for the Reds after a three match winless run.
And it was wideman Miles who popped up with a brace to secure three valuable points for Stanley - and also upset former England caretaker boss Peter Taylor in his first game in charge of the Bantams.
"The last time I scored two was for Macclesfield against Accrington so it was a long time ago," said Miles. "I should score more and it was a big result for us as we needed the win."
Stanley boss John Coleman said: "We performed well and we deserved the three points. John Miles took both his goals well. John always has the ability but doesn't score enough goals and he could have had a hat-trick. He is a big talent and once he gets going he is hard to stop.
"At 1-0 I was slightly nervous as we lost a 1-0 goal lead on Tuesday so at 2-0 it was certainly easier for me."
New boss Taylor got a good reception from the visiting fans who were packed into two sides of the Crown Ground for Stanley's biggest league crowd of the seasonof 3,396.
The first half was largely forgettable although Bobby Grant came close with a volley in the early stages and Bradford defender Zesh Rehman was saved from embarrassment on 24 minutes when a Luke Joyce free kick came off
the defender's head and wasn't far off a goal.
After that, it was a story of penalty appeals to the end of the first half with Stanley furious they didn't get one of three they shouted for from referee Trevor Kettle.
First Andy Procter felt he had his shirt tugged when leaping for a header; then Matthew Clarke challenged Grant in the area but the whistle was blown for off-side.
And then Grant and Rehman tangled in the box with Grant left on the floor but once again the referee wasn't having any of it.
But Stanley almost suffered minutes after the re-start as Bradford carved out their best opening. Captain Simon Ramsden's free
kick into the area was flicked on and it fell for top scorer James Hanson a couple of yards from goal but he amazingly fired over the bar to Coleman's relief.
And minutes later Grant fed through Miles, City were looking for off-side but he ran clean through to fire past Matt Glennon for the opening goal.
Taylor put on three subs but it was Stanley who continued to take charge. Miles came close again with Matt Glennon parrying his effort away while he skied another effort and Jimmy Ryan flicked over in a good position.
And Miles made it safe four minutes from time from a tight angle after getting on the end of Symes' cross.