Resuming at 22-1, Australia lost four wickets, two each to paceman Rahat Ali and left-arm spinner Zulfiqar Babar as Pakistan tightened their grip after posting a big first innings total of 570 at Sheikh Zayed Stadium.
Clarke was unbeaten on 34 with Mitchell Marsh on eight as Australia, trailing the series 0-1, need another 251 runs to avoid the follow on.
Australia will hope Clarke, who flopped in the 221-run defeat in the first Test in Dubai with scores of two and three, bats longer to avoid further trouble.
Resuming at 22-1, Australia lost David Warner in the sixth over of the day when the left-hander played straight into the hands of point on a short delivery from Rahat.
Glenn Maxwell, who made 37, tried to take the attack to the bowlers with two boundaries and hit a six off Babar but the veteran spinner had the last laugh when he spun one across the bat to hit the off stump.
From the other end Rahat bowled nightwatchman Nathan Lyon on 15 before Babar trapped Steven Smith for a duck, leaving Australia tottering at 100-5.
Babar has figures of 2-43 and Rahat 2-23.
Younis Khan hit an epic double hundred in Pakistan's big total on Friday which also had centuries from skipper Misbah-ul Haq and Azhar Ali.

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