In the other match of the day, which was also curtailed by bad weather at the start, Scotland beat Fiji by 21 runs, but not receiving a scare from the first-timer.
South Africa, chasing the West Indies' 153 for nine in 35 overs, appeared to have the game in hand when it began the final over needing just seven runs with seven wickets in hand.
But fast bowler Keemo Paul claimed a wicket and conceded only six runs to conjure an exciting tie. Wiaan Mulder remained unbeaten on 58 as South Africa finished with 153 for four.
In the other match, Scotland elected to bat first and piled up 192 for eight in 36 overs with Rory Johnston making 53 and Finlay McCreath chipping in with 36. Fiji's seamer Josaia Baleicikoibia took three for 26.
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Fiji made a gallant attempt to surpass the stiff target before being bowled out for 171 in the 32nd over. Opener Delaimatuku Maraiwai scored 57 and tail-ender Tuwai Yabaki smashed an unbeaten 36 off 16 balls that contained five boundaries and two sixes.
The 11th edition of the biennial 16-nation tournament features nine Test-playing nations and seven Associate and Affiliate Members - Afghanistan, Canada, Fiji, Namibia, Nepal, Ireland and Scotland.
Teams have been divided into four groups with the top two in each advancing to the Super League quarter-finals and the other two qualifying for the Plate championships.