The wicketkeeper struggled behind the stumps but made 75 in a match-winning partnership with Chris Woakes.
The pair turned the tables at Old Trafford with a 139-run stand which turned the tables on the tourists.
The pair shared a half-century stand at better than a run a ball to keep an unlikely run-chase alive.
Chris Woakes Stuart Broad and Ben Stokes help out as the tourists struggle second time around.
Babar hit 11 boundaries of the highest order in an unbeaten stay of exactly 100 balls.
Pakistan made a solid start after deciding to bat first.
Pakistan elected to bat under grey skies at Old Trafford.
He took 26 wickets at 16.73 against Pakistan four years ago and is relishing facing them again.
He weighed in with 11 wickets in the second and third Tests against the West Indies at Old Trafford.
Stuart Broad and Chris Woakes staked their claims in the convincing third Test victory over the West Indies but competition is fierce.