In reply, Sri Lanka were bowled out for 203 in 41.3 overs with only Captain Upul Tharanga (57), Niroshan Dickwella (41) and Kusal Perera (44 not out) providing some resistance against the South African bowlers.
Sri Lanka decided their best route towards the target was to attack the South African bowlers from the outset.
The leg-spinner took 4 wickets in the innings to completely destroy the Sri Lankan batting line-up and help his team notch a comprehensive win.
South Africa have won 34 of their 65 ODI matches against Sri Lanka, including in their most recent meeting in February. Then Chandi was run out and Kapugedera was dismissed soon afterwards.
However, South Africa then made hay as Amla and Francois du Plessis added 145 runs for the second wicket - Lasith Malinga costing his side dear when he dropped Du Plessis at long-leg when he was on eight.
Sri Lanka were cruising along at 116 for two when Tahir was introduced to the attack in the 18th over and South Africa immediately got a firm grip on the game.
In terms of the number of innings required to reach the 25-century milestone, Amla is comfortably out on his own.
Sri Lanka were also missing their captain and key player Angelo Matthews who is expected to return for the next game, his return will provide the Lankan lions with some much needed stability and experience in the middle-order.
Amla's 103, his 25th one-day global ton, should have been the platform for a heftier target in glorious sunshine on a flat Oval pitch. But the press conference of AB de Villiers was the praise of both the heroes of Hashim Amla and Imran Tahir.
Underlining the blow this represents for Sri Lanka, Tharanga was the country's best batsman and the only one to reach a half-century against South Africa.
That was the end of the foyrth over and next ball Alex Hales, trying to drive Rabada, got an outside edge to Amla and England were 15 for four.
Left-arm spinner Keshav Maharaj proved an effective deputy when called upon by the Proteas during their recent 2-1 ODI series defeat by England but skipper AB de Villiers was glad to have Tahir available following a hamstring tweak.
After their first match against the Proteas on June 3, they will next face India (June 8) and Pakistan (June 12).
And worse was to come for South Africa when Amla, going for a second, was well short of his ground and run out by Kusal Mendis.
South Africa may have lost their one-day global series to England prior to the ICC Champions Trophy but AB de Villiers insists there are still reasons to be confident ahead of their tournament opener against Sri Lanka.
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