Brisbane:David Warner set up the innings with a chance-filled 94 and Travis Head took over with an unbeaten century after a mini-collapse in the middle order to guide Australia to 343-7 at stumps on Day 2, a 196-run lead in the Ashes series opener.
Warner had a big reprieve on 17 off a no-ball from Ben Stokes, one of the many times the England allrounder overstepped but one of the few he was called for. Warner was also dropped in the slips on 48 and narrowly avoided being run out as he scrambled back to his crease on 60.
But he ran out of luck after sharing partnerships of 156 with Marnus Labuschagne (74) for the second wicket and 23 with Steve Smith (12) for the third, finally out just after the tea interval when Ollie Robinson took two wickets with consecutive deliveries.
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Robinson had Warner caught in the covers by Stokes and then bowled Cameron Green, who didn't play a shot to a ball that hit his off stump, in a period when Australia slid from 189-2 to 195-5.
New wicketkeeper Alex Carey successfully blocked the hat-trick ball, his first delivery in test cricket, but was out for 12 as England clawed back to have the Australians at 236-6.
Head and captain Pat Cummins combined in a 70-run stand that restored Australia's domination of the first two days at the Gabba, accelerating the scoring as England's fielding got ragged.
The partnership ended when England skipper Joe Root picked up the wicket of his counterpart, having Cummins caught at leg slip.
Head continued with Mitchell Starc and was on 96 when he attempted a sweep to Root, was hit on the arm and Burns couldn't reach as the ball ballooned down the leg side.
He reached his century from 85 deliveries with a driven boundary off Chris Waokes in the first over with the new ball, an innings containing 12 fours and two sixes.