James Taylor, seeking a maiden test century, was unbeaten on 74 and Jonny Bairstow was 37 not out.
Their stand for the fifth wicket was worth 83 at the close.
Pakistan, hoping to maintain their impressive record since moving matches to the United Arab Emirates, won the second test after the first was drawn.
England eventually had the better of a slow day's play, in which only 48 runs came in the middle session.
Starting the day at four for no wicket, they lost Moeen Ali cheaply for 14, falling with a cross-batted slog at Shoaib Malik.
That was the only wicket to fall before lunch, although Alastair Cook and then Joe Root perished in quick succession soon after the interval.
Cook was outsmarted again by Yasir Shah, who had dismissed him in both innings of the previous test.
The England captain was one run short of his 46th test fifty when he tried to glance a delivery from the leg spinner but only managed to deflect it onto his pads before Azhar Ali took the catch at forward short leg.
Root (four) soon joined him back in the pavilion after wicket-keeper Sarfraz Ahmed took a low, one-handed catch off Rahat Ali to leave England 97 for three.
Taylor, returning to test cricket after an absence of three years, and Ian Bell saw them through to tea, only for Bell to be smartly stumped off Yasir for 40.
That was Pakistan's last success of the day, however, Bairstow accompanying Taylor through to the close to leave England in the driving seat.
(Writing by Steve Tongue, editing by Stephen Wood)
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