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.
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.
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.
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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