An early double strike by fast bowler James Anderson, followed by a superb piece of fielding by Ben Stokes to run out Mohammad Hafeez, raised England's hopes with Pakistan at one stage on 3-2 in its second innings. But Younis and Misbah stabilised the innings to give Pakistan a 27-run lead at the interval.
Resuming today on 569-8, England declared its first innings on 598-9 to take a 75-run lead in reply to Pakistan's 523-8.
Masood played on to Anderson again, but unlike the first day when a slower bouncer hit him on the helmet before rolling onto the stumps, it was off the toe of his bat this time as he tried to defend.
Four balls later, Anderson's bouncer reared up at Malik and all he could do was fend it off to Jonny Bairstow at short-leg.
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At 47-3, Hafeez was third to depart, a victim of Stokes' brilliance in the field. The batsman pushed Adil Rashid's delivery to point and there was hesitation as they set off for a run. Stokes swooped on the ball, picked it up with his left hand, transferred it to his right and hit the wicket at the non-striker's end in one action.
Earlier, England captain Alastair Cook called in his last pair after 45 minutes of batting, with Stuart Broad not out on 17 and Anderson on three.
Only one England wicket fell in the morning, Rashid clean bowled by an Imran Khan in-cutter for 12 with the score on 590.
Pakistan has played seven test matches at the Sheikh Zayed Stadium, winning four, including the last two by massive margins against Australia (356 runs) and New Zealand (248 runs) and drawing the other three.