After resuming on 6-253 overnight, with Nathan Lyon claiming five wickets on day one, the off-spinner picked up where he left off, claiming two more scalps to finish with figures of 7-94.
Ashton Agar claimed two scalps, while Warner produced an impressive run out for the remaining wicket.
Mushfiqur Rahim returned to the crease on 62 not out, while Nasir Hossain was unbeaten on 19.
Rahim did not last long on day two, with Lyon clean bowling him for 68. Hossain then put on a handy 28-run partnership with Mehedi Hasan, but when the former was removed for an impressive 45, which included five boundaries, Australia cleaned up the tail with relative ease.
Australia’s innings got off to the worst possible start, losing opener Matt Renshaw caught behind down the leg side for just four in the second over.