Calvin Zola's double gave Burton a one-goal lead to take into the second leg of this League Two play-off semi-final.
The 28-year-old striker headed the Brewers ahead in the 23rd minute before curling in a second six minutes later.
A Nahki Wells penalty, after Damian McCrory handled in the area, got the hosts back into the tie but Robbie Weir's strike made it 3-1 at the break.
Garry Thompson halved the deficit with a thunderous 25-yard drive that skimmed off Gary Jones on its way into the net.
Underdogs Burton were appearing in the Football League play-offs for the first time but they showed no signs of nerves, despite their hosts going into the tie in a rich vein of form, having won five of their last nine.
The Brewers took the lead when the excellent Jacques Maghoma escaped the attentions of two Bradford players to cross in for Zola to head home.
Record breaking Bradford
The crowd at Valley Parade of 14,657 is a record for a League Two play-off semi-final first leg.
Gary Rowett's side doubled their advantage in highly controversial circumstances.
Zola appeared to be offside when Zander Diamond sent a deep ball into the box but the flag stayed down and the Congolese striker did brilliantly to drift inside and find the net.
Burton, who only missed out on automatic promotion by two points, should then have had a third but midfielder John McGrath was denied by home goalkeeper Jon McLaughlin.
Bradford were given a much-needed lifeline in the 39th minute when Wells converted from the spot for his 23rd goal of the season after McCrory handled Thompson's powerfully struck shot.
The Burton defender was lucky not to have been shown a red card for the offence, and the visitors took full advantage of their good fortune just before the break by grabbing a third goal.
Alex MacDonald was released down the right and slid a ball into the path of Weir, who was able to fire home at the near post.
The second half was less eventful, but Thompson restored some hope for Bradford with 16 minutes remaining when he pounced on a visibly tiring Burton defence.
The former Scunthorpe man cut in from the right and hit a fierce drive past Stuart Tomlinson that keeps alive Bradford's dreams of reaching Wembley for a second time this season, following their Capital One Cup Final defeat by Swansea.
Bradford City manager Phil Parkinson:
"After the way we played in the first half I'm glad we're only one goal behind.
"The play-offs can do strange things and we got punished.
"It was one of our poorest displays defensively. We were really poor and we didn't work as a unit.
"This group of players has been tremendous and we need another great performance on Sunday."
Burton Albion manager Gary Rowett:
"We planned all week to be chasing the game in the second leg so for it to be tight is a bonus. I can't say I'm disappointed with the score.
"People expected us to come here and be very defensive.
"The tie is very even now and I don't think it matters to us who are favourites.
"People might think it is only the League Two play-offs but this matters an awful lot to a lot of people."
Live Text Commentary
Full Time The referee blows for the end of the match.90:00 +6:04
Alan Connell produces a right-footed shot from the edge of the box and misses to the left of the goal.90:00 +3:48
Foul by Damien McCrory on Garry Thompson, free kick awarded. Rory McArdle restarts play with the free kick.90:00 +2:05
Centre by James Meredith, Effort from the edge of the area by James Hanson goes wide of the right-hand post.90:00 +1:36
Foul by Billy Kee on Nathan Doyle, free kick awarded. James Meredith restarts play with the free kick.88:30 Substitution
Substitution Alex MacDonald leaves the field to be replaced by Adam Drury.88:03 Substitution
Substitution (Bradford) makes a substitution, with Alan Connell coming on for Nahki Wells.86:14
Foul by Damien McCrory on Stephen Darby, free kick awarded. Gary Jones restarts play with the free kick, Rory McArdle produces a header from deep inside the six-yard box that clears the bar.84:43
The free kick is swung in right-footed by Gary Jones, save by Stuart Tomlinson.84:43 Booking
Booking The referee books Alex MacDonald for unsporting behaviour.84:32
Free kick awarded for a foul by Alex MacDonald on Kyel Reid.79:08
Inswinging corner taken right-footed by Alex MacDonald from the right by-line.78:13
Direct free kick taken by Damien McCrory.78:13 Booking
Booking Stuart Tomlinson receives a yellow card for time wasting.77:55
Rory McArdle challenges Billy Kee unfairly and gives away a free kick.76:55
Nahki Wells fouled by Damien McCrory, the ref awards a free kick. Shot comes in from Nahki Wells from the free kick.76:10
Shot by Alex MacDonald.75:38
Nahki Wells has a curled shot. Save by Stuart Tomlinson.73:47 Goal scored
Goal! - Garry Thompson - Bradford 2 - 3 Burton Goal scored by Garry Thompson from outside the penalty area to the top right corner of the goal. Bradford 2-3 Burton Albion.70:54
Marcus Holness takes a shot. Gary Jones takes a outswinging corner.
Foul by Damien McCrory on Stephen Darby, free kick awarded. Jon McLaughlin takes the direct free kick.68:27
Shot from just outside the penalty box by Nathan Doyle misses to the left of the target.68:12
Alex MacDonald gives away a free kick for an unfair challenge on Kyel Reid. Free kick taken by James Meredith.66:27
Free kick taken by Stuart Tomlinson.66:27 Substitution
Substitution Billy Kee on for Calvin Zola.66:27
James Hanson challenges Ian Sharps unfairly and gives away a free kick.64:45
Corner taken by Alex MacDonald, Rory McArdle manages to make a clearance.62:21
Effort from the edge of the area by Garry Thompson goes wide of the left-hand post.61:30
James Hanson challenges Zander Diamond unfairly and gives away a free kick. Stuart Tomlinson takes the free kick.58:05
Foul by Damien McCrory on Garry Thompson, free kick awarded. Rory McArdle restarts play with the free kick.57:38
Robbie Weir takes a shot. Save by Jon McLaughlin.56:27 Substitution
Substitution (Bradford) makes a substitution, with Nathan Doyle coming on for Ricky Ravenhill.56:27 Substitution
Substitution Kyel Reid on for Will Atkinson.53:02
Free kick awarded for an unfair challenge on Zander Diamond by Nahki Wells. Stuart Tomlinson restarts play with the free kick.49:00
The ball is delivered by Alex MacDonald, Close range header by Calvin Zola goes wide of the left-hand post.47:13
Foul by Michael Nelson on John McGrath, free kick awarded. Jacques Maghoma produces a shot on goal direct from the free kick.45:53
Jacques Maghoma delivers the ball, clearance by Will Atkinson.45:01
The second half begins.45:00 +3:03 Half time
Half Time The whistle is blown to end the first half.45:00 +2:32
Shot from just outside the penalty area by Jacques Maghoma misses to the left of the target.45:00 +1:35
The ball is crossed by Nahki Wells.45:00 +0:43
The referee gives a free kick against Calvin Zola for handball. Jon McLaughlin takes the direct free kick.44:16
Foul by Gary Jones on Zander Diamond, free kick awarded. Stuart Tomlinson takes the direct free kick.43:03
The assist for the goal came from Alex MacDonald.43:03 Goal scored
Goal! - Robbie Weir - Bradford 1 - 3 Burton Robbie Weir finds the back of the net with a goal from deep inside the penalty box to the bottom right corner of the goal. Bradford 1-3 Burton Albion.39:57
Gary Jones has a shot on goal from outside the box which misses left.37:07 Goal scored
Goal! - Nahki Wells - Bradford 1 - 2 Burton Placed penalty scored by Nahki Wells. Bradford 1-2 Burton Albion.34:36
The free kick is delivered right-footed by Gary Jones from right wing, clearance by Damien McCrory. The referee gives a against Robbie Weir for handball.34:36 Booking
Booking Marcus Holness receives a caution.34:22
Unfair challenge on Garry Thompson by Marcus Holness results in a free kick.34:01
The ball is delivered by Nahki Wells, Damien McCrory manages to make a clearance.33:04
John McGrath takes a shot. Save made by Jon McLaughlin.31:40
Centre by Garry Thompson, Damien McCrory gets a block in.31:09
The ball is crossed by Jacques Maghoma.29:59
Foul by John McGrath on Will Atkinson, free kick awarded. Gary Jones crosses the ball from the free kick right-footed from left channel, save made by Stuart Tomlinson.27:40 Goal scored
Goal! - Calvin Zola - Bradford 0 - 2 Burton Calvin Zola fires in a goal from the edge of the penalty area to the bottom right corner of the goal. Bradford 0-2 Burton Albion.25:50
Foul by Marcus Holness on Garry Thompson, free kick awarded. The ball is delivered by Gary Jones, Header on goal by Rory McArdle from inside the box goes harmlessly over the target.24:14
The ball is sent over by Nahki Wells, clearance by Ian Sharps.22:46
Alex MacDonald takes a shot. Save by Jon McLaughlin.21:23
The assist for the goal came from Jacques Maghoma.21:23 Goal scored
Goal! - Calvin Zola - Bradford 0 - 1 Burton Calvin Zola scores a headed goal from inside the six-yard box. Bradford 0-1 Burton Albion.21:07
Jacques Maghoma delivers the ball,19:57
Unfair challenge on Jacques Maghoma by Ricky Ravenhill results in a free kick. Direct free kick taken by Stuart Tomlinson.18:10
Free kick awarded for a foul by Will Atkinson on Marcus Holness. Stuart Tomlinson takes the free kick.17:28
Calvin Zola has an effort at goal from deep inside the area missing to the left of the target.14:04
Foul by Nahki Wells on Anthony O'Connor, free kick awarded. Stuart Tomlinson takes the direct free kick.12:55
Ricky Ravenhill gives away a free kick for an unfair challenge on John McGrath. Stuart Tomlinson takes the direct free kick.11:50
Will Atkinson produces a right-footed shot from outside the penalty box and misses left.8:20
Alex MacDonald takes a shot. Jon McLaughlin makes a save. Unfair challenge on John McGrath by Nahki Wells results in a free kick. Free kick taken by Anthony O'Connor.7:52
Centre by James Meredith, save by Stuart Tomlinson.7:12
Inswinging corner taken by Gary Jones from the right by-line.5:13
Garry Thompson takes a shot. Inswinging corner taken right-footed by Gary Jones, Stuart Tomlinson makes a save. Outswinging corner taken by Gary Jones from the right by-line, Ian Sharps manages to make a clearance.3:30
Michael Nelson fouled by Calvin Zola, the ref awards a free kick. Free kick taken by Jon McLaughlin.2:24
Jacques Maghoma fouled by Rory McArdle, the ref awards a free kick. Shot on goal comes in from Jacques Maghoma from the free kick.0:00
The game gets underway.
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