Pakistan were 61-2 at the close in their second innings with Azhar Ali unbeaten on 21 and Younis Khan on 16 after another batting collapse saw Australia almost squander any chance of levelling the series.
Australia were dismissed for 261 in their first innings, 309 behind Pakistan's first innings total of 570-6 declared, but Misbah-ul Haq did not enforce the follow-on and chose to bat again so as to set a big target on the fourth day.
Pakistan won the first Test by 221 runs in Dubai.
Mitchell Johnson (2-29) gave the Pakistanis an early scare with the wickets of Ahmed Shehzad (14) and Mohammad Hafeez (three) but Ali and Younis ensured Pakistan did not surrender their strong position.
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Australia once again failed to post a big total, with Mitchell Marsh hitting 87 and Michael Clarke scoring 47.
Australia had hoped skipper Clarke, who managed just two and three in the first Test, would bat long enough to counter the Pakistan attack but he fell after a good start.
Clarke added 64 for the sixth wicket with Marsh.
Marsh batted solidly and hit a six off Babar and then took three runs to complete his half-century off just 56 balls.
But wickets fell at regular intervals, with Yasir Shah dismissing Brad Haddin (10) and Johnson for a duck to leave Australia struggling at 199-8.