Paul Sykes scored a hat-trick as Bradford produced a late flourish to hold off battling Wakefield for a second successive engage Super League win.
The Wildcats dominated for long spells and were denied three times by video referee Richard Silverwood as they battled back from 20-6 down to get within four points.
But Michael Worrincy finished off the Wildcats five minutes from time before Sykes darted over for his third in the closing moments at Murrayfield.
The Bulls' six tries came in pairs early on, just before half-time and right at the end of the second Magic Weekend match.
In between Wakefield were the better side and the scoreline could easily have been different.
The Bulls made the better start and opened the scoring when Steve Menzies and Ben Jeffries combined to send Sykes racing over.
Wakefield almost responded immediately as Dave Halley, who began the season on loan with the Wildcats, dropped a high kick.
Richard Moore drove forward from the resulting possession but Halley redeemed himself with a superb tackle to deny the prop.
Bradford made the most of the reprieve to score a minute later when scrum-half Paul Deacon, back after a month out injured, put Jamie Langley through a gap and Newton finished under the posts.
Wakefield were denied by the video referee after Tony Martin slid onto a kick but just failed to touch down before the ball ran dead.
Wildcats scrum-half Danny Brough then had a fine try chalked off after Danny Sculthorpe was ruled to have impeded Newton in the build-up.
John Kear's men finally got on the scoreboard just before the half-hour after Sam Obst was felled by a high tackle and Jason Demetriou shrugged off three defenders to reach the line.
Bradford's response was impressive as Sykes hit a Jeffries pass at speed to claim his second try and Menzies scored a scintillating fourth.
Menzies started and finished a move which saw Rikki Sheriffe speed down the touchline and offload for Sykes, who in turn flicked out a fine pass for the scorer.
Sheriffe should have scored again before the hooter but spilled a Jeffries kick.
Wakefield started the second half strongly but were soon on the wrong end of another Silverwood review.
Kear was left shaking his head after Dale Ferguson was ruled to have strayed offside just before touching down from a Brough kick.
Yet Wakefield were also frustrated by some outstanding defending until Steve Snitch finally rewarded them for their efforts when he wriggled his way over 15 minutes from time.
The Wildcats sensed an opportunity and continued to pound the Bulls line.
They set up a grandstand finish when Matt Blaymire brilliantly chipped a Brad Drew kick over his own head and scored.
Martin's conversion cut the deficit to four points but Bradford roused themselves at the last and secured victory as Worrincy ran in three minutes from time.
Sykes then finished the job as time ran out with Deacon adding his fourth conversion.