Amla scored 66 in South Africa’s total of 279 for eight in 48.2 overs to reach 5000 runs in 101 innings, well ahead of the previous record of 114 jointly held by West Indies great Viv Richards and Indian batsman Virat Kohli.
With their target cut to 225 in 32 overs, West Indies collapsed after the loss of blazing opener Chris Gayle to end 164 all out from 28.2 overs and slip to a 61-run defeat on the Duckworth/Lewis method.
South Africa won the toss and elected to bat, but made a poor start when they slumped to 16 for two.
Two big partnerships involving top-scorer AB de Villiers (81) repaired the early damage though as he put on 99 with Amla and 123 with powerful left-hander David Miller (70).
A torrential downpour ended the innings 10 balls shy of the allotted overs and when play resumed two hours and 43 minutes later, the tourist were handed a stiff revised target.
Gayle (41), so scintillating in the recently completed Twenty20 series, blazed away but lost his wicket when attempting an ugly baseball swipe at a Dale Steyn delivery. He was caught behind by De Villiers.
With him went the West Indies hopes but they did not help themselves with more poor shot selection.
Nobody else managed a significant contribution as the Proteas bowlers squeezed the run rate higher and picked up wickets at regular intervals.
West Indies handed a debut to left-handed batsman Jonathan Carter (17) but he was stumped off leg-spinner Imran Tahir, who continued his good form in the shorter formats with three for 30 in six overs.
Steyn was another top performer with the ball, collecting three for 27 from 5.2 overs.
The second game in the five-match series will be played in Johannesburg on Sunday. (Reuters)