Pakistan were bowled out for 400 in reply to England's first innings 297, a significant lead of 103 runs.
The tourists kept England in the field for nearly 10-and-a-half hours in total.
England's cause was hampered when James Anderson, their all-time leading Test wicket-taker, was barred from bowling again in the innings after receiving a third warning for running on the pitch from the umpires, with Pakistan then on 368 for eight.
With the four-Test series all square at 1-1, Pakistan resumed on 257 for three after Azhar Ali had been dismissed for 139 off the last ball of Thursday's play, following partnerships of 181 and 76 with Sami Aslam (82) and Younis Khan (21 not out), respectively.
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Younis was joined in the middle by fellow veteran Misbah.
Woakes, who had dismissed Azhar, struck again when he had Younis caught behind for 31 glancing down the legside.
But two balls later Misbah, showing the value of patience and good judgement, drove Broad down the ground.
Broad though found his range when a full-length delivery smashed into Asad Shafiq's off stump for an 18-ball nought to leave Pakistan 296 for five, still one run behind.
Misbah's single to third man off Broad saw Pakistan into the lead.
Pakistan's batsmen have found Moeen Ali to their liking this series and Misbah reverse-swept him four when the off-spinner came on before lunch.
At lunch, Pakistan were 336 for five, a lead of 39 runs.
Misbah was 44 not out and Ahmed a typically brisk 20 not out off 27 balls.
After lunch Misbah -- who scored a century during Pakistan's 75-run win in the first Test at Lord's -- posted his third fifty this series when he drove Anderson for a sixth four in 93 balls.
But on 56 he was bowled playing down the wrong line to Anderson to end a useful stand of 62 with Ahmed.