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.
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 Woakes in the first over with the new ball, an innings containing 12 fours and two sixes.
Head was felled by a full-toss from Mark Wood when he was on 105, hit on the glove and helmet before falling to the ground, but recovered to finish unbeaten on 112 at stumps.
Warner's survival and Stokes' delivery stride were the two main talking points on Thursday.
Warner got his first reprieve from the TV umpire after being beaten by Stokes, bowling his first over in a test match since March.
TV broadcaster Channel 7 showed Stokes had also overstepped the crease on his previous three deliveries and not been called by the umpires. The Ashes broadcaster later revealed Stokes had overstepped the front crease 14 times in the opening session on Day 2 and had only been called twice for a no-ball.
Cricket Australia said a technology problem at the Gabba meant that the third umpire, Paul Wilson, couldn’t review TV replays of every delivery to check if bowlers were over-stepping the crease, leaving it to the on-field umpires to make the calls.
Robinson returned the best figures for the England bowlers, taking 3-48 from 18 overs on an extended second day, and also having a chance put down.
Left-arm spinner Jack Leach picked up the key wicket of Labuschagne, but was otherwise punished by the Australian batting lineup and returned 1-95 from 11 overs.
Stokes was restricted to just nine overs and conceded 50 runs, appearing to be struggling with his fitness when he bowled late with the old ball.
