Chasing a mammoth target of 474 runs to win, the hosts failed to counter South Africa's bowling attack and were eventually collapsed to 133 all out in their second innings on the fourth day.
Resuming the fourth day at 1-0, England lost four wickets before lunch and the remaining six before tea.
Vernon Philander was the pick of the bowlers for his figures of three for 24 followed by left-arm spinner Keshav Maharaj's three for 42.
Duanne Olivier bagged two wickets in two balls to dismiss Mark Wood and James Anderson.
Chris Morris also took two wickets by giving away just seven runs.
Earlier, opener Dean Elgar (80) and first drop Hashim Amla (87) not only notched up blistering half-century each, but they also stitched a huge 135-run stand for second wicket to guide South Africa to a huge second innings score of 343 for 9 declared.
Skipper Faf du Plessis (63) and Philander (42) also made significant contributions in their side's innings.
Philander was declared 'Man of the Match' for his all-round performance.
The two sides will now take on each other in the third Test, beginning July 27 at the Oval.
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