Fast bowler Morne Morkel ripped through England's middle-order with three wickets in six balls, and there was a wicket apiece for pacemen Wayne Parnell and Dale Steyn.
Off-spinner JP Duminy delivered the final blows, taking the last two wickets.
South African captain Graeme Smith said his team had at last got the result they wanted after letting England off the hook in two of the previous Tests.
"We feel very happy and, if I'm honest, we could easily be sitting here 3-1 up. We just lacked the knockout blows in Centurion and Cape Town," Smith told a news conference.
"England showed great resilience and played very well in Durban (to win the Test) but we've played the better cricket in three of the Tests."
England began the day on 48 for three, still trailing by 195 runs, but the fire and intensity of Morkel and Steyn's bowling meant there was no respite for their batsmen.
It was left-arm paceman Parnell, playing in his first Test, who made the initial breakthrough as Kevin Pietersen, who scored just three runs on Sunday to go to 12, chased after a delivery angled across him and edged a catch to wicketkeeper Mark Boucher.
Morkel was then able to make serious inroads in his second spell of the day, Ian Bell (5), Matt Prior (0) and Stuart Broad (1) all being caught behind the wicket off deliveries that reared up nastily off the pitch.
Graeme Swann swung lustily in scoring 20 before an excellent away-swinger from Steyn had him caught at third slip.
Paul Collingwood was the one England batsman to prosper, making a defiant, counter-attacking 71 before he pulled a long-hop from off-spinner Duminy straight to deep backward square-leg. Duminy then completed the victory when he bowled Ryan Sidebottom for 15.
Morkel ended with figures of four for 59 in 16 overs, and was seven for 98 in the match.
England skipped Andrew Strauss blamed his team's defeat on the opening day of the Test when they were bowled out for 180.
Score Board
England (I Innings): 180
South Africa (I Innings): 423/7 decl.
England (II Innings, O/n: 48/3)
Strauss lbw Parnell 22
Cook c Smith b Morkel 1
Trott c De Villiers b Steyn 8
Pietersen c Boucher b Parnell 12
Collingwood c Morkel b Duminy 71
Bell c Kallis b Morke 5
Prior c Smith b Morkel 0
Broad c Boucher b Morkel 1
Swann c De Villiers b Steyn 20
Sidebottom b Duminy 15
Anderson (not out) 1
Extras (lb-6, W-1, nb-6) 13
Total (all out, 42.5 overs) 169
Fall of wickets: 1-6, 2-21, 3-48, 4-84, 5-103, 6-103, 7-104, 8-134, 9-154.
Bowling: Dale Steyn 14-1-64-2, Morne Morkel 16-5-59-4, Wayne Parnell 8-1-17-2, McLaren 3-1-13-0, Duminy 1.5-0-10-2.
