At tea, Younis Khan (30) and Misbah-ul-Haq (three) were at the crease as Pakistan reached 92-3, giving them an overall lead of 228 with seven wickets intact at Dubai stadium.
James Anderson provided England with a much-needed early wicket when he had Shan Masood caught behind for one, dismissing the Pakistani opener for the fourth time in four innings.
Seamer Mark Wood then chipped in with the wickets of Shoaib Malik (seven) and Mohammad Hafeez (51) to help England stage a comeback.
Malik flopped for the third time after scoring an epic 245 in the first Test -- his first in five years -- bowled by Wood who also had Hafeez caught at slip.
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Earlier paceman Wahab Riaz (4-66) and leg-spinner Yasir Shah (4-93) helped Pakistan dismiss England for 242 after they had resumed on a well-placed 182-3.
Pakistan had made 378 in their first innings.
Riaz initiated the collapse, in which England lost their seven remaining wickets, for 60 runs as he bowled with venom and guile to dismiss a dangerous looking Joe Root (88), Ben Stokes (four) and Jos Butler (nought) in an incisive spell.
England had hoped their batting would rally around the fast-rising Root who added two boundaries off Shah in the fourth over of the day to his overnight score of 76.
But Riaz found the edge of Root's bat with a sharp outswinger to give Pakistan the much-needed breakthrough. Root smashed 12 boundaries during his 141-ball knock.
Bairstow survived some close calls and was surprisingly given not out by television umpire Chris Gaffaney of New Zealand when replays showed Younis Khan had taken the edge off Shah in the first slip.
In between, Riaz had Stokes and Butler caught behind in successive overs.