Seeking to level the three-match series after losing the second Test in Dubai, England were kept in the hunt by Anderson who took 4-17 to dismiss Pakistan for a paltry 234 on a relaid Sharjah stadium pitch.
At the close, England openers Alastair Cook (nought) and Moeen Ali (four) had survived two overs to finish on four without loss as England trail by 230 runs.
Anderson's new-ball partner Stuart Broad kept the pressure on from the other end, bowling eight of his 13 overs maiden and finishing with 2-13.
Misbah added a fighting 80 for the sixth wicket with Sarfraz Ahmed (39) but all the other batsmen, including Younis Khan (31), Shoaib Malik (38) and Mohammad Hafeez (27), failed to capitalise on good starts.
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England took the second new ball with the score on 222-7 with Anderson dismissing Misbah caught in the slips before wrapping up the innings with the wicket of Rahat Ali for four.
Misbah hit seven fours and two sixes during his 160-ball knock but could not stop the slide as Pakistan lost their last five wickets for just 38 runs.
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Younis, who made a brilliant hundred in the second Test in Dubai, looked in good shape before falling leg-before as he missed an incoming full toss from Anderson and unsuccessfully challenged umpire's decision.