South Africa had been set an unlikely 492 to win by Joe Root and were rather more interested in batting the remain four sessions of the match to save the game.
But Ben Stokes, having already made a first-innings hundred, took two wickets in two balls to leave the tourists struggling at 117/4.
And the swashbuckling all-rounder was at the centre of the action as England finished off the game on Monday, taking three excellent slip catches off the bowling of Moeen Ali before the off-spinner trapped Morne Morkel to complete a dramatic hat-trick.
Dean Elgar had survived the first session of South Africa’s efforts to get away from London with a draw despite having been hit on the hand, a blow with the coaching staff admitted might have broken bone.
The 30-year-old will undergo a scan this week to decide whether he will be able to play in the fourth and final Test of the series at Old Trafford, which starts on Friday, and if he does, he will do so having earned the respect of the England team.
He withstood a barrage of short bowling on days four and five, going on to make a fine century.
But when Elgar fell with 136 to his name, at last tempted into a drive by Moeen which he could only edge to Stokes at slip, it proved the end of South Africa’s resistance.
Kagiso Rabada fell the very next ball in a live action replay of the previous dismissal before an over later with his very next ball, Moeen reviewed an LBW decision and was rewarded with his fourth wicket of the innings.
