The hosts won by 61 runs according to the Duckworth/Lewis method when the tourists were bowled out for 164. South Africa made 279 for eight before their innings was cut short by rain after 48.2 overs yesterday.
Chasing a reduced target, which eventually became 225 runs off 32 overs after another brief interruption, Gayle led the West Indies to a storming start as he and Dwayne Smith put on 51 for the first wicket inside the first six overs.
He hit two fours in Steyn's first over -- one a top edge over wicketkeeper AB de Villiers -- but swung once too often and edged a catch to De Villiers.
Leon Johnson was dismissed in the next over by Vernon Philander and the West Indies lost wickets at regular intervals as they fell further and further behind the asking rate.
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"We made a start but lost our way in the middle," said new West Indies captain Jason Holder.
"There was a lot happening in that wicket," he said.
South Africa were rocked by two early wickets and were pegged back towards the end of the innings but runs flowed freely in between as De Villiers shared partnerships of 99 with Amla and 123 with Miller, both at slightly better than a run a ball.
Amla and De Villiers, South Africa's champion batting pair, came together with the total 16 for two in the fifth over and the runs soon started to flow.
The left-handed Miller made 70 off 68 balls before his dismissal, with the total on 238 in the 40th over, sparking a collapse in which five wickets fell for 41 runs in 9.2 overs.
De Villiers followed soon afterwards after making a relatively restrained 81 off 94 balls.