Burns, playing in only his third Test match but his first as opener, blasted spinner Mark Craig for two sixes over long off to race from 88 to 100 in three balls.
When bad light stopped play, Australia had stretched their overall lead to 503 runs at 264 for four and an overnight declaration imminent with first-innings centurion Usman Khawaja not out nine and Adam Voges on one.
Warner sprinted to his second century of the match with 116 before he gave his wicket away with a switch hit off spinner Mark Craig.
It was only the third time that a batsman has scored a Test century in both innings on three separate occasions along with Ricky Ponting and Sunil Gavaskar.
It was also the first time any opening pair had compiled 150-run plus partnerships in each innings of a Test match.
It was the fourth century of the Test after Warner (163) and Khawaja (174) in Australia's first innings and Kane Williamson's defiant 140 in New Zealand's innings.
Skipper Steve Smith completed a low scoring match when he was given out for one to a close-to-the-ground catch by Williamson off Trent Boult that needed a lengthy umpire's review.
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