Spinner Nathan Lyon grabbed the wicket of debutant opener Sharjeel Khan for 40, caught at mid-wicket, nearing stumps to have Pakistan at 55 for one.
At the close, Pakistan's leading series scorer Azhar Ali was not out 11 with nightwatchman Yasir Shah on three.
Skipper Steve Smith called a halt to Australia's second innings at 241 for two with 16 overs left on the fourth day and the tourists facing the herculean task of scoring 465 for victory.
"I think the position we're in is pretty good, the way the guys batted today, especially Davy Warner, to get those runs as quickly as possible and do some pretty unselfish batting," paceman Josh Hazlewood said.
"The wicket's still pretty good, but I think there's enough there to create nine more chances, if it's reverse swing or spin."
Smith was out in a review after 'Hot Spot' detected a faint edge off his glove and was caught behind off Yasir for 59 off 43 balls to finish the series with 441 runs at 110.25.
The explosive Warner smashed leg-spinner Yasir for six, six, four, four in the fourth over of the innings, and then clouted Imran Khan for four consecutive boundaries in the seventh over.
His breathless half-century came off 23 balls with seven fours and three sixes and was the second fastest in Test history after Pakistan skipper Misbah-ul-Haq's 21 balls against Australia in Abu Dhabi in 2014.
But Warner perished when he missed in a lusty swing and was bowled by Wahab Riaz for 55 off 27 balls. Younis Khan was left unconquered on 175 as Pakistan lost their last two wickets in an hour's play post-lunch after rain washed out the first session.
"It will not be easy because the fifth day old Test match and we play in Sydney and they have two spinners and good fast bowlers as well."
Younis was dropped on 141 by wicketkeeper Matthew Wade, who got his right glove to the chance but could not cling on, much to bowler Mitchell Starc's annoyance.
Wade was forced off during Thursday's play with a stomach illness but returned to the game on Friday.
Yasir gave Smith his ninth catch of the series when he was picked up in the slips off Josh Hazlewood for 10 before Imran Khan was bowled two balls later for a duck.
"I love to perform for my country, for my team and whenever my team needs me, it's a little bit late this time, but I am a proud Pakistani," Younis said.
The tourists on 315 finished 223 runs in arrears, but skipper Smith did not enforce the follow-on.
Hazlewood finished with four wickets for 55 and spinner Nathan Lyon captured three for 115.
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