Pakistan dismissed Australia for 261 runs to take a first-innings lead of 309. Captain Misbah-ul Haq could have enforced a follow-on, but opted to bat again and set an even bigger target for the opposition.
In the second innings, Pakistan reached 61-2, losing the two openers in the 21 overs possible before stumps.
More frustratingly for Australia, Younis Khan, who has now made centuries in each of the three innings of the series, was still out there on 16, with Azhar Ali giving him company on 21 after fast bowler Mitchell Johnson removed the opening batsmen quickly.
Pakistan batting coach Grant Flower defended Misbah's decision not to enforce the follow-on.
"I wasn't surprised by the decision, some of our bowlers were tired," Flowers said. "I think Misbah wanted to make sure there was only one winner in the match by batting again. We will bat till lunch and then try to bowl them out."
Australia's fate was more or less sealed by their inept batting display. The pitch at Sheikh Zayed Stadium still played fair but the Australians showed a distinct lack of application as wickets kept falling at regular intervals.
Mitchell Marsh, playing in only his second match for Australia, looked the most comfortable on the crease and was rewarded with his first half century. The 23-year-old son of former Australian star Geoff Marsh was finally dismissed for 87 when he pushed Imran Khan's full toss to Rahat Ali at mid-wicket.
"I was really disappointed that I got out that way," Marsh said. "I just tried to play my natural game. I wasn't thinking much. I was just trying to put it out of mind that wickets were falling around me."
Imran was the most successful Pakistan bowler with 3-60, including a great delivery to remove Australian captain Clarke, who was looking dangerous on 47.
After putting together 64 runs for the sixth wicket with Marsh - the best partnership of the innings - Clarke was completely foxed by Khan's delivery that pitched way outside the off stump and swung back to take his middle stump.
David Warner (19) was the first batsman to go Saturday morning, smashing a wide delivery from Ali straight into the hands of Yasir Shah at point. The opener could add only three runs to his overnight score of 16.
Glenn Maxwell, who came into the side at the expense of Alex Doolan, was deceived by Zulfiqar Babar when he stepped out once too often and was clean bowled for 37 which came in just 28 balls.
Nightwatchman Nathan Lyon vigil's came to an end on 15 when Rahat found a way through his forward defensive shot while Steve Smith did not have the time to settle down before he was trapped leg before wicket by Babar.
A draw or a win would give Pakistan a rare series win over Australia. Pakistan has beaten Australia five times before at home, but its last series victory came 20 years ago in 1994.