The Bantams made it to the home of football earlier this season when they famously reached the Capital One Cup final, but they were undone by a superb first-half showing from the Brewers, who go into Sunday's second leg firm favourites.
Calvin Zola was the chief destroyer as he helped himself to a six-minute double with a bullet header and then a delightful curled effort.
In a frantic opening period, the Bantams hit back through Nahki Wells' penalty before the visitors again went two in front, courtesy of Robbie Weir's drilled finish.
Phil Parkinson's men did at least salvage some hope when Garry Thompson scored from distance with a fine effort to reduce their arrears - but Burton return to home soil, where they won 17 of 23 games in the regular campaign, with their lead intact and confident of gracing the Wembley turf themselves.
Having lost only one of their last nine games of the regular campaign, Bradford were the form team going into the play-offs and they were backed by a boisterous home crowd hungry for another night like those against Arsenal and Aston Villa in the League Cup.
But after a cagey opening, Burton had clearly not read the script and took the lead in the 22nd minute with a goal created by the fine wing play of Jacques Maghoma.
He picked up the ball on the left, found a yard of space and delivered a delightful ball that Zola headed in at the far post with power.
It got even better six minutes later as Zola, this time his own architect, stunned Valley Parade.
The striker picked up the ball at the far post and cut inside to curl a superb effort past Jon McLaughlin, although replays suggested he was offside.
The Brewers, who were beaten here in the league 11 days ago and in the early part of City's League Cup run, were in dreamland and it could have been even better when a slick passing move cut Bradford wide open and John McGrath was denied by the body of McLaughlin.
But 10 minutes later the Bantams hauled themselves back into the contest from the penalty spot.
They broke down the left, the ball fell to Thompson who thrashed a shot into the body of Damien McCrory, with referee James Adcock judging the defender to have handled.
Wells stepped up and coolly sent Stuart Tomlinson the wrong way from 12 yards.
However, the home resurgence was short-lived as the visitors restored their two-goal cushion two minutes before the break when Weir drilled home from 14 yards after Alex MacDonald's cross to put Burton in the box seat and leave Bradford exiting the pitch at half-time to boos.
Despite the hosts' need for to rescue something out of the second period it was Burton that continued to look more dangerous with Zola heading wide and then McGrath forcing McLaughlin into a sprawling save.
After the visitors took Zola off, Bradford seized the initiative and laid siege on Burton's goal - and Thompson got a potentially vital effort with 20 minutes remaining, the former Scunthorpe man curling a sumptuous 25-yard shot home.
The Brewers had barely been out of their half for 20 minutes, but MacDonald had an instant chance to hit back, although his effort from 14 yards clipped the top of the bar.
Burton survived a late onslaught to prevail and take a precious lead back to Staffordshire.