The pair shared in a record third-wicket stand of 247 as the Proteas romped to 361-5 off their 42 overs – the rain-affected match was reduced by eight overs earlier in the day after the start was delayed by more than two hours.
Coming together on 59-2, Amla struck 133 off 105 deliveries, hitting 11 fours and six sixes. The less-experienced Rossouw was even more brutal, hitting 132 from 98 balls, blasting nine fours and eight sixes.
Man-of-the-match Rossouw’s ton was his second in ODIs, while Amla became the fastest batsman to reach 19 hundreds in the one-day game, bringing it up in his 107th international match.?? ?? ?? ?? ?? ?? ????
Their third-wicket partnership off just 63 balls beat, by nine runs, the previous best by a South African pair while becoming the second highest of all time behind the 258 scored by Darren Bravo and Denesh Ramdin for the West Indies against Bangladesh last year.
Both men fell to Andre Russell whose three wickets came at a cost of 85 runs from eight overs.
The tourists never looked like causing too many problems for the South African bowlers and got off to the worst possible start, losing Chris Gayle first ball of the innings – caught behind by wicketkeeper Quinton de Kock off Kyle Abbott.
Marlon Samuels top-scored with 50 off 47 but, when he was dismissed in the 28th over with the score on 172-4, Windies still required 189 more runs from 87 deliveries.
They were finally all out for 230 in the 38th over.