Chasing 303, Pakistan slipped to 77-3 before Sarfraz Ahmed (90) and Shoaib Malik (77) shared 163.
Despite a late wobble, the tourists got home with 10 balls to spare.
England's 302-9 came via 87 from Jason Roy and Ben Stokes' 75, but they took only 42 runs off the last eight overs in a slide of five wickets for 64.
They were stifled by some impressive pace bowling from Hasan Ali, who took 4-60, and Mohammad Amir (3-50).
