The 39-year-old batsman 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 Shah 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.
Younus becomes first person to score a century in all 11 countries
Younus remained unbeaten off 334 balls with 17 fours and three sixes, and was given a big ovation from the SCG crowd as he left the ground after his 34th Test century.
"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," said Younus.
Regarding Pakistan's chances in the match, he added, "We want to finish this Test series on a good note. 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."
Hazlewood finished with four wickets for 55 and spinner Nathan Lyon captured three for 115.
Yasir Shah’s reaction to national anthem is all you need to see today
The tourists on 315 finished 223 runs in arrears, but skipper Smith did not enforce the follow-on.
Later on, 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.
Usman Khawaja was left unbeaten on 79 off 98 balls and Peter Handscomb was on 40 off 25 balls. Handscomb finished with a series average of 114.66.
"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," said paceman Josh Hazlewood.
"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."
Warner made us look foolish, says Wahab
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.
David Warner smashed the second fastest 50 in Test history to give Australia a flying start in their chase for runs and a declaration.
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.
At the end of day's play, Australia were nine wickets away from a series clean sweep and Pakistan an improbable 410 runs from victory in the match's final innings.
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.
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