Pakistan dominated the morning session when they beat England for 275 points, but their target of 355 points meant they needed to break a home record to tie the series.
They also seemed ready for the task, but the English tailors conjured three magic deliveries after the lunch break to regain the initiative.
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The seesaw contest changed its complexion again in the final session following a 108-run partnership between Imam, who fell just before the close for 60, and Saud.
Saud was undefeated on 54 with Faheem Ashraf on three at stumps.
Pakistan, who finished the third day with a score of 198-4, are still 157 points from their goal.
Earlier, England added 73 runs to their overnight score of 202-5 on Matchday 3 at Multan Cricket Stadium.
Ben Stokes (41) needed 43 balls to score his first boundary and was the first to fall, digging deep to trigger a collapse.
Spinner Abrar Ahmed picked up his 11th wicket on his first Test by knocking Ollie Robinson through the gate.
Overnight batsman Harry Brook (108) hit his second hundred of the series before leg spinner Zahid Mahmood (3-52) finished the England tail.
The Pakistani spinners took 18 of England’s 20 wickets – with the other two sold out.
The hosts had to rearrange their opening pair following a hamstring issue with Imam.
They promoted the struggling Mohammad Rizwan, who hit a flurry of limits early in his stroke to transfer the pressure to England.
James Anderson retired Rizwan for 30 minutes after lunch with a peach of a delivery that tipped and beat the outside edge to hit the stump.
Robinson produced an equally stunning ball to fire Pakistan captain Babar Azam for one.
Babar shouldered arms for a delivery outside the stump but stepped back to shake off his stumps.
Abdullah Shafique made 45 but couldn’t shield his off-stump from Mark Wood’s pace and movement.
Imam arrived at number five and reignited Pakistan’s pursuit with Saud.
It would have been the Pakistan session, but spinner Jack Leach eventually had Imam caught in the slides to break the partnership.