Burnley made a bright start enjoying most of the possession. After only two minutes Lee Briscoe screwed a 25-yard shot wide before Gareth Taylor saw his header go past the post when Glen Little set him up with a cutback from the by-line.
City created their first opportunity after 11 minutes when Robert Molenaar tested Marlon Beresford with a well-struck drive from 30 yards.
Taylor tried his luck, drilling an angled shot beyond the far post as the Clarets continued to hold the upper hand.
But it was City who broke the deadlock against the run of play with the best move of the half.
Wayne Jacobs picked up the ball on the left and a played a neat one-two with Andy Myers.
Jacobs then raced to the by-line before putting the ball back across the box. Danny Cadamarteri latched on to it before finding Andy Gray, who side-footed home from six yards.
But City then shot themselves in the foot when they found themselves down to ten men after defender Mark Bower was ordered off for his second bookable offence in the 35th minute.
After the break, Burnley boss Stan Ternent tried to inject some pace into his side by taking off Dmitrios Papadopoulos and Mark McGregor for Robbie Blake and Alan Moore.
Ten minutes after the re-start Cadamarteri received his marching orders for apparently elbowing Dean West and City were made to pay when Burnley levelled shortly before the hour mark. Blake pulling the trigger with a low shot which took a deflection off Myers before nestling in the bottom corner.
It was only a matter of time before Burnley took the lead and it finally came after 76 minutes.
Little swung over a deep cross from the right to find Taylor who powered a header from the edge of the six-yard box, beyond Davison.
Bradford never gave up the fight though, grabbing an equaliser in the last minute.
Sub Claus Jorgensen saw his shot blocked by the keeper. Fortunately for City, he was given a second bite of the cherry. This time he fired a shot from the tightest of angles. His effort came off the near post and rolled across the face of the goal before Michael Proctor slammed the ball into the empty net.
After the game Ternent said: "We were coasting in the last few seconds of the game. We made a blunder. We were punished for it."
Bantams boss Nicky Law was proud of his players. He said: "Their commitment could not be faulted today. We had to keep going. They had a lot of possession but they rarely put us under pressure."