Pakistan were dismissed for just 198 in reply to England’s huge 589 for eight declared — a deficit of 391 runs. Yet Cook decided against asking Pakistan to bat again.
England had the fifth biggest first-innings lead without enforcing the follow-on in Test history.
Two of those instances had come in ‘timeless’ Tests, while the others were when Australia led England by 445 runs in Brisbane in 2006 and 398 at Adelaide in 2013 — with the Australians winning both of those Ashes matches.
Cook’s decision, with England 1-0 down in the four-match series, seemed all the more curious given rain had stopped play for an hour earlier on Sunday.
Another rain interruption forced an early tea, with England 11 without loss in their second innings. Cook, who made 105 in the first innings, was nine not out and Alex Hales two not out.
Earlier, England all-rounder Chris Woakes took four for 67, while Joe Root followed his first-innings 254, his Test-best score, with four catches at second slip.
Misbah-ul-Haq, the Pakistan captain, top-scored for his side with 52 and shared a ninth-wicket stand of 60 with Wahab Riaz, who made a Test-best 39.
Pakistan, who resumed on 57 for four, saw their first-innings collapse continue in Sunday’s morning session as they lost a further four wickets for 62 runs to be 119 for eight at lunch.
But with Cook opting against using the experienced new ball duo of James Anderson and Stuart Broad after lunch, Pakistan added 79 runs in the second session.
Pakistan started Sunday’s play with opener Shan Masood 30 not out and Misbah one not out.
Anderson, England’s all-time leading wicket-taker, marked his return to Test cricket on his Lancashire home ground after missing Pakistan’s series-opening 75-run win at Lord’s last week with a shoulder injury by taking the first wicket to fall on Sunday.
Left-handed opener Masood had held firm for more than two hours in all. But having moved on to 39, Masood exited in familiar fashion when he edged Anderson to Root.
Pakistan were now 71 for five, their total at the rain break. Shortly after play resumed, Asad Shafiq fell for four when he drove loosely at a Broad slower ball and lobbed a catch to Hales at point.
Sarfraz Ahmed may have come in at 76 for six but the wicket-keeper stuck to his attacking game and got off the mark when he cut Broad over Hales’s head for four.
By contrast it took Misbah 47 balls to score the first boundary of his innings, a square-drive off Anderson. Woakes, who took 11 wickets in defeat at Lord’s, saw his first over Sunday cost 11 runs as Sarfraz hit two well-struck boundaries.
But when Sarfraz (26) played defensively at Ben Stokes, he succeeded only in giving Root another easy slip catch.
Misbah completed a 108-ball fifty before, sweeping once too often at off-spinner Ali, he was caught at short fine leg by Cook.
Wahab hoisted Ali for six. But going for another big hit off the spinner, he holed out to end a 61-ball innings that also featured five fours.