The West Indies, whose innings was disrupted by two rain breaks, posted 234-3 after 45.3 overs with Deandra Dottin making an unbeaten 150.
Needing a DLS-revised target of 204, the Proteas were in big trouble on 87-5 after 17.4 overs before rain ended proceedings.
Tazmin Brits top-scored for the hosts with 32 off 37 balls.
The second of four ODIs will take place at the Wanderers on Monday.