Pakistan, who declared their first innings on 570-6, did not force the follow-on even though Australia fell 110 runs short of the mark and decided instead to set them a target to chase.
Mitchell Johnson removed both their openers in the second innings, but Pakistan, who comprehensively won the first test in Dubai, stretched their overall lead to 370 at the close.
Younus Khan, who has hit 106, 103 not out and 213 in his last three innings in the series, was unbeaten on 16 with Azhar Ali on 21.
The Pakistani bowlers had earlier generated enough turn, bounce and reverse swing from a lifeless track to run through the tourists.
Imran Khan claimed three for 60, impressing both with the new and old ball, while fellow paceman Rahat Ali and the spin duo of Zulfiqar Babar and Yasir Shah claimed two wickets apiece.
David Warner, who had started Australia’s reply with three fours in Imran’s first over on Friday, chased a short and wide Rahat delivery to find the point fielder and depart on 19.
There was never any doubt about Glenn Maxwell’s aggression but a brisk 37 failed to answer the lingering questions about whether the 26-year-old has the temperament to succeed at test level, especially in the crucial number three position.
Before being dismissed by Rahat, Nathan Lyon survived several leg-before appeals as Pakistan resisted wasting reviews on a nightwatchman.
They did not hesitate, however, to seek a review to dismiss the scoreless Steve Smith, who was hit on the pad by a Babar delivery.
Clarke, who added 64 runs with Marsh for the sixth wicket, looked decisive against the spinners, taking big strides and using his feet to get to the pitch of the ball.
It was reverse swing, which ultimately proved his undoing.
After repeatedly failing to middle Imran’s reverse-swinging balls, Clarke had his middle stump pegged back by one that curved back from outside the off stump and went through the bat-pad gap.
Brad Haddin braved a shoulder injury that had forced him off the field on Friday to contribute 10 runs before leg-spinner Shah’s double strike deepened Australia’s crisis.
Marsh fell 13 runs short of his maiden test century, hitting a full toss from Khan to the mid-on fielder to depart after a defiant knock that included 13 fours and a six.
(Reporting by Amlan Chakraborty in New Delhi; Editing by Toby Davis)