Queensland 6 for 307 (Heazlett 70, Labuschagne 67, Burns 54*, Wildermuth 51, Conway 3-72) defeated New South Wales 5 for 305 (Jack Edwards 84, Bertus 69*, Stanlake 2-49) by four wickets
Chasing 306 on a good surface at Allan Border Field, the Bulls had slipped from 2 for 179 in the 26th over to 5 for 199 in just 24 balls, and their eight-game losing streak against the Blues looked in danger of becoming nine.
But Wildermuth, with a previous highest score of just 13 in Australia's one-day domestic competition, and Burns, batting at No.5 in a revamped Bulls line-up, compiled an 83-run stand to help steer the home side to victory.
Wildermuth, who does have two first-class hundreds, struck the ball with tremendous power to make 51 from 56 balls before Sean Abbott bowled him through the gate with 24 still required from 24 balls.
Burns remained composed reaching his half-century with a slog sweep for six off Arjun Nair, and Mark Steketee clubbed 15 not out from six balls to see the Bulls home with 12 balls to spare. Wildermuth was named Player of the Match.
The Bulls needed some help from New South Wales to get there. Kurtis Patterson dropped Burns with 28 runs to win, spilling a simple skied pull shot in the ring at midwicket.
Jack Edwards had also missed a straightforward chance at second slip off Abbott in the opening over of the chase. Sam Heazlett's outside edge went straight through his hands at thigh height.
Heazlett made them pay with a blistering half-century. He smashed 70 from 57 balls with nine fours and two huge sixes. Heazlett was hitting the ball hard and he nearly hit Mickey Edwards square in the face in his fifth over. Edwards was fortunate to get his hand in front of his face and walk away with just a bruise.
Heazlett formed a 112-run stand with Marnus Labuschagne who also compiled an excellent half-century at better than a run-a-ball as the Bulls charged well ahead of the required rate. Heazlett fell lbw to debutant Nathan McAndrew before Harry Conway delivered an inspired spell to swing the momentum back the Blues' way.
He clean bowled Matt Renshaw with a well disguised slower ball yorker before Labuschagne picked out McAndrew at backward point. Jimmy Peirson then ran himself out next ball after a loud lbw shout caused some confusion. He charged off for a non-existent run as Burns watched on in bewilderment at the non-striker's end. Abbott swooped in from cover to complete the run-out by running the ball to the stumps.
Burns kept his cool with Wildermuth. They took advantage of the fact McAndrew was forced off the field with a back spasm, which caused Blues captain Peter Nevill to turn to some part-timers while the partnership built and the game slipped away from there.
Earlier, half-centuries to 19-year-old Jack Edwards, 26-year-old debutant Nicholas Bertus and veteran Moises Henriques helped the Blues to a competitive total of 305 after being sent in to bat on a tacky surface that flattened out as the day progressed.
The Blues looked on for a monstrous total when they cruised to 1 for 172 in the 33rd over. Queensland failed to make the most of the early morning moisture missing their lengths as Daniel Hughes and Edwards rolled to a 51-run opening stand.
But then Billy Stanlake, who was held back early, removed Hughes in his first over forcing a mistimed a drive on the up to cover. Stanlake delivered four overs in his first spell, taking 1 for 7, but then did not bowl again until the 33rd over.
It allowed Edwards and Henriques to compile a 122-run stand. Edwards overcame a sluggish start to pass fifty for the third time in his short career. He drove powerfully down the ground and was savage on anything under-pitched. Henriques picked apart the spin of Matthew Kuhnemann and Labuschagne to build a superb platform for the visitors.
But when Peirson turned back to Stanlake, the game changed again. Edwards was bounced out, top edging a hook to fine leg failing to control the extra pace and bounce. Stanlake finished with 2 for 49 from 10 overs while the rest of his team-mates conceded more than five-an-over.
Henriques top-edged a sweep off Kuhnemann in the next over to put the brakes on the Blues' charge.
But Bertus, a left-hander who was on List A debut after playing just one Sheffield Shield game last season, played a brilliant hand late in the innings to tip the Blues total over 300. He struck seven fours and two sixes, targeting the short boundaries at midwicket and extra cover, to smack an unbeaten 69 from just 60 balls. But 305 always seemed just under par and the Bulls made the most of the better batting conditions in the afternoon.