Ben Jeffries returned to Belle Vue to haunt his old club with a match-changing contribution.
Elliot Whitehead did more than his share to ensure the Bulls' victory with his hat-trick, but two of those tries - and two others besides - came from the pin-point kicking of Jeffries in his first appearance of the season.
It made the difference between a game that Wakefield really ought to have won and one that ran away from completely in the second half. After their dismal performance against Wigan last week, it was a startling Bradford transformation.
As in that match, the Bulls began dreadfully, conceding a try within the first minute. Ali Lauitiiti began it with one of his trademark offloads, Isaac John kicked into space and Ben Cockayne scored with some ease.
With a heavy penalty count against them and the Wildcats looking inventive and enterprising, the game was already drifting away from the Bulls.
Jeffries kept them in it with his first demonstration of the kicker's art, chipping the ball perfectly for Keith Lulia to catch and touch down.
It was the first of five times that the lead was to change hands.
The second came when Danny Washbrook's intelligent pass put the Wakefield captain, Steve Southern, through a gap.
The game continued its see-saw rhythm when Whitehead claimed his first, and interception from John.
That was enough to put the Bulls ahead, slightly against the run of play at half time, but they fell behind immediately after when Danny Kirmond stormed through some ineffectual tackling.
The game swung, however, on four Bulls tries in 13 hectic minutes.
Three of them came from virtually identical kicks from Jeffries, who probed away relentlessly like a boxer who has found a fatal flaw in his opponent's defence. Wakefield seemed to have defused the first of them, but it popped out for Brett Kearney to force down.
The next two were plucked out of the air by the alert Whitehead and when Kearney sneaked in for his second, the game was as good as won.
"It was a well deserved win," said the Bulls' coach, Mick Potter. "We fixed up a few things after last week."
Richie Mathers got one back for Trinity, but their coach, Richard Agar, blamed "a simple failure to defend kick-plays.
"There were signs at half time that we weren't doing what we needed to. "Bradford came with a very simple game-plan and made it work."
Agar refused to blame the massive turn-around in personnel - there are 18 new players in the Wakefield squad this season - for their inconsistency.
"We just needed a few players playing a bit better tonight," he said.
Wakefield Mathers; Fox, Collis, Mellars, Cockayne; John, Smith; Wilkes, Aiton, Southern, Kirmond, Lauitiiti, Washbrook. Subs used: Wood, Raleigh, Johnson, Trout.
Bradford Kearney; Kear, Platt, Lulia, Crookes; Sammut, Jeffries; Kopczak, Diskin, Hargreaves, Bateman, Whitehead, Langley. Subs used: L'Estrange, Scruton, Joseph, Burgess.
Referee B Thaler (Whitehaven).