Amla made exactly 100 as South Africa declared their second innings closed on 301 for seven, leaving England a target of 364 for victory and 96 overs to survive for a draw.
England were 11 for one after six overs at the close after Morne Morkel had captain Andrew Strauss caught behind for a single to complete a day of dominance for the South African team.
Mark Boucher scored 63 not out off 73 balls and Morkel lashed four boundaries in his unbeaten 22 not out off 13 deliveries, the flurry of runs enabling South Africa to declare 37 minutes before stumps.
James Anderson was the best of the England bowlers, taking four for 73 in 20.5 overs.
South Africa, leading by 62 runs on first innings, were in early trouble on 46 for four before Amla and AB de Villiers put on 119 for the fifth wicket.
James Anderson struck in the third over of the day when nightwatchman Paul Harris was bowled off his thigh pad for 11. South African captain Graeme Smith never looked comfortable against accurate bowling by Anderson and Graham Onions on a pitch of unpredictable bounce and he fell to Onions five overs later when he pushed forward defensively and was bowled off an inside edge for 12.
First innings century maker Jacques Kallis made only four while Amla remained unflappable.
Score Board
SOUTH AFRICA (I innings) 418
ENGLAND (I innings) 356
SOUTH AFRICA (II innings) o/n 9-1
Prince b Anderson 0
Smith b Onions 12
Harris b Anderson 11
Amla b Anderson 100
Kallis c Cook b Broad 4
AB de Villiers c Bell b Broad 64
Duminy lbw b Anderson 11
Boucher (not out) 63
M Morkel (not out) 22
Extras (LB-10, W-4) 14
Total (7 wkts decl in 85.5 overs) 301
Fall of wickets: 1-2, 2-20, 3-34, 4-46, 5-165, 6-191, 7-266, Bowling: Anderson 20.5-1-73-4, Onions 16-3-50-1, Broad 16-5-58-2, Swann 27-3-91-0, Collingwood 6-1-19-0.
ENGLAND (II innings)
Strauss c Boucher b Morkel 1
Cook (batting) 4
Anderson (batting) 6
Extras 0
Total (for 1 wicket in 6 overs) 11
Fall of wickets: 1-5. Bowling: Ntini 2-1-5-0, M Morkel 3-1-6-1, Harris 1-1-0-0.
Deccan Herald is on WhatsApp Channels| Join now for Breaking News & Editor's Picks