Resuming at 222-4, England lost both its overnight batsmen James Taylor and Jonny Bairstow in quick succession in the morning session.
Samit Patel then tried to steady England's innings with an unbeaten 41 before Adil Rashid fell in the last over of the session with England leading by 51 runs.
Patel, who came ahead of the injured Ben Stokes in the lineup, got England past Pakistan's first innings total of 234 with a pulled boundary off Ali's short delivery.
Shoaib Malik also helped to slow England's momentum just before lunch when Rashid prodded at the offspinner's delivery and Azhar Ali scooped a one-handed diving catch at forward short leg.
In his comeback match after three years, Taylor had provided England an invaluable 89-run fifth-wicket stand with Bairstow on Monday, hitting six boundaries in a 161-ball knock that spanned over 3 and a half hours.
Bairstow was then clean bowled by Babar for 43, giving the left-arm spinner his first wicket in 31 overs.
It was still uncertain if Stokes would bat for England after falling awkwardly and damaging his right shoulder while attempting to catch Ahmed on Sunday.
Scans revealed the all-rounder has a collar bone joint injury and the England and Wales Cricket Board said in a statement that he will be unable to bowl or field the remainder of the test match, but he may bat if needed.
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