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 as 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.
The opener was 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.
The striker then collected the ball at the far post and cut inside to curl a superb effort past Jon McLaughlin, although replays suggested he was offside.
In a frantic opening period, the Bantams hit back through Nahki Wells' penalty after Damien McCrory was adjudged to have handled before the visitors again went two in front, courtesy of Robbie Weir's drilled finish from Alex MacDonald's cross.
Phil Parkinson's men did at least salvage some hope when 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.