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.
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.
The West Indies, which was sent into bat, was steered to a challenging total by Keacy Carty’s 45 and an unbeaten 33 off 34 balls by tail-ender Michael Frew.
In the other match, also in Fatullah, 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.
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.
For Scotland, Haris Aslam claimed four wickets for 39 runs and Mitchell Rao took three for 22.
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.
South Africa tied with West Indies in Fatullah
West Indies 153-9, 35 overs (Keacy Carty 45, Michael Frew 33 not out; Conor McKerr 3-30, Dayyaan Galiem 2-30)
South Africa 153-4, 35 overs (Wiaan Mulder 58 not out)
Scotland beats Fiji by 21 runs in Fatullah
Scotland 192-8, 36 overs (Rory Johnston 53, Finlay McCreath 36; Josaia Baleicikoibia 3-26)
Fiji 171 all out, 31.3 overs (Delaimatuku Maraiwai 57, Tuwai Yabaki 37 not out; Haris Aslam 4-39, Mitchell Rao 3-22)
Monday’s warm-up matches:
Afghanistan v New Zealand, BKSP-1
Sri Lanka v Nepal, BKSP-2
Ireland v Canada, BKSP-3
India v Pakistan, BKSP-4
Zimbabwe v Namibia, Chittagong
England v Bangladesh, Chittagong