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."
- 01 McLaughlin
- 02 Darby
- 03 Meredith
- 22 Nelson
- 23 McArdle
- 04 Ravenhill (Doyle - 57' )
- 11 Thompson
- 14 Atkinson (Reid - 57' )
- 18 Jones
- 09 Hanson
- 21 Wells (Connell - 89' )
- 12 Duke
- 16 McHugh
- 07 Reid
- 24 Doyle
- 10 Gray
- 17 Connell
- 20 Hines
- 13 Tomlinson Booked
- 14 McCrory
- 20 O'Connor
- 21 Holness Booked
- 24 Sharps
- 05 Diamond
- 06 McGrath
- 08 Weir
- 19 Maghoma
- 10 Zola (Kee - 67' )
- 26 MacDonald Booked (Drury - 89' )
- 16 Lyness
- 03 Webster
- 17 Phillips
- 27 Drury
- 18 Paterson
- 29 Kee
- 30 Symes