Victory put Pakistan 1-0 up in the three-game series and maintains their record of never having lost a series in their adopted home of the United Arab Emirates.
Starting the final day on 130 for three and chasing an unlikely 491 for victory, England slumped to 193 for seven after lunch.
Adil Rashid (61) and Stuart Broad (30) then added 60 in 90 balls before the latter was bowled by an inswinging Wahab Riaz yorker.
Undeterred, Rashid and Mark Wood (29) were adroit in defence as Pakistan captain Misbah-ul-Haq switched between pace and spin to try to end their resistance.
His team’s appeals grew more desperate as the overs ticked by and the game entered the final hour with two wickets remaining.
Seven fielders crowded the batsmen and the pressure told when Wood edged Zulfiqar Babar’s turning ball to Mohammad Hafeez in the gully.
Five overs later Rashid was last man out, caught attempting a drive through the covers off Yasir Shah.
