Anderson dismissed opener Shan Masood (one) and Shoaib Malik (nought) in the third over as Pakistan's second innings started disastrously on a weary Sheikh Zayed Stadium pitch.
Mohammad Hafeez (32) and Younis Khan (two) restored calm, but Pakistan still trailed by 40 after England took a 75-run lead in the first innings.
Read: Cook's double ton frustrates Pakistan in first Test
England announced closure of their first innings at 598-9 in reply to Pakistan's 523-8 declared.
That left the first Test heading for a tame draw, barring an extraordinary Pakistan collapse in the second innings, which initially looked possible.
Masood, who was bowled after a short delivery from Anderson deflected onto the stumps from the grill of his helmet in the first innings, played on to the same bowler.
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Malik, who scored a career best 245 in the first knock, lasted three deliveries before Anderson's bouncer surprised him as his evasive shot landed safely in Jonny Bairstow's hands.
Younis also survived a shaky start, but Hafeez, fresh from his 98 in the first knock, hit four boundaries and a six to ease some of the pressure.
Earlier, England, resuming at 569-8, lost Adil Rashid for 12 in the seventh over of the day, bowled by paceman Imran Khan who finished with 2-74.
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Stuart Broad (17) and Anderson (three) remained unbeaten as England batted for a marathon 206 overs on a flat pitch, with skipper Alastair Cook knocking an epic 263 on Friday.
Left-arm paceman Wahab Riaz was the pick of Pakistan bowlers with 3-125 while spinner Zulfiqar Babar finished with 1-183 off 72 overs.
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