Duanne Olivier was the man of the series against Pakistan after taking 24 wickets at an average of 14.70.
Starting the day on 153 for three, Pakistan lost their remaining seven wickets for 120 runs to be bowled out for 273.
Set to make a daunting 381 to win, Pakistan were 153 for three at the close, needing another 228 runs.
Faf du Plessis' decision to pick an all-pace attack paid dividends with all four fast bowlers picking up wickets.
England, set a mammoth 474 runs for victory, collapsed to 133 all out in their second innings 40 minutes before tea on the fourth day.