Babar hit 11 boundaries of the highest order in an unbeaten stay of exactly 100 balls.
Mark Wood finished the job.
Pakistan made a solid start after deciding to bat first.
Pakistan elected to bat under grey skies at Old Trafford.
The England and Yorkshire fast bowler saw his career cut slightly short by injury problems.
Nagging uncertainty over Stokes’ recent quad injury means England will not know how to balance their side until the eleventh hour.
Paul Stirling and Andrew Balbirnie both hit centuries in the shock victory.
Stuart Broad took his 500th Test wicket last month.