Stafanie Taylor, batting at number three, top-scored with 75 from 78 balls while opener Kycia Knight got 46 and Shemaine Campbelle 33.
Teenaged leg-spinner Dane van Niekerk continued her success against the Windies with three for 47 while seamer Marizanne Kapp supported with two for 42.
Earlier, Trisha Chetty hit 45 and Cri-zelda Brits, 44, as South Africa were restricted to 230 for seven off 50 overs after opting to bat first.
van Niekerk finished on a brisk 33 not out off just 30 balls while captain Mignon du Preez chipped in with 31.
Right-arm pacer Treymane Smartt led the attack with two for 43 and Taylor’s ten overs of off-spin proved effective and yielded just 32 runs, even though she went wicket-less.
Yolandi Potgieter fell in the tenth over for seven as South Africa got off to a slow start at 22 for one but Chetty and du Preez repaired the damage in a 62-run, second-wicket partnership.
When both perished within four overs of each other, Brits and Kapp added 40 for the fourth wicket to steady the innings.
The right-handed Brits was aggressive in striking four boundaries and two sixes off just 41 balls but was part of a slide that saw three wickets tumble for 28 runs.
It was left to van Niekerk to keep the Proteas going at the end with an innings that included two fours and a six.
West Indies then suffered an early setback when they lost Natasha McClean for five to the eighth ball of the innings at 15 for one but Taylor and Kycia Knight posted an impressive 126 for the second wicket to put their side back on top.
The right-handed Taylor struck nine fours and a six while Kycia faced 68 balls and counted six boundaries.
However, van Niekerk accounted for both in the space of 11 balls – Kycia caught and bowled and Taylor holing out in the deep – to leave the Windies on 146 for three in the 26th over.
Deandra Dottin played the only way she knows how to, slamming four fours in a cavalier 24 from 21 balls and adding 27 for the fourth wicket with Kyshona Knight (4).
However, she paid the price for her adventure when she was brilliantly taken on the ropes at long on by Marcia Letsoalo at 173 for four, leading to another slump as Kyshona followed next over with no runs added.
Campbelle, who struck six fours in her 42-ball stay at the crease, ignored the clatter of wickets around her to carry West Indies to the brink of victory before also succumbing.
West Indies will now turn their attention to Australia in their second game on Wednesday in Mumbai.
In other Super Sixes matches played:
Australia 147 (Coyte 44, Sthalekar 41, Shrubsole 3-24) beat England 145 (Greenway 49, Ferling 3-35) by two runs.
New Zealand 108 for 2 (Mackay 39*, Bates 37) beat Sri Lanka 103 (Tahuhu 4-27, Ruck 3-16) by eight wickets.
SOUTH AFRICA innings
Y. Potgieter c Taylor b Daley 7
T. Chetty b Dottin 45
M. du Preez c Dottin b Quintyne 31
M. Kapp c Kycia A. Knight b Taylor 12
C. Brits run-out 44
S. Benade c wkp. Aguilleira b Smartt 3
D. van Niekerk not out 33
S. Fritz c Taylor b Smartt 19
S. Ismail not out 9
Extras: (lb-8, w-16, nb-3) 27
Total: (7 wkts, 50 overs) 230
Fall of wickets: 1-22 (Potgieter), 2-84 (du Preez), 3-100 (Chetty), 4-140 (Kapp), 5-162 (Benade), 6-168 (Brits), 7-199 (Fritz).
Bowling: Smartt 10-043-2 (w-2, nb-2), Daley 10-1-39-1 (w-1), Munroe 6-0-25-0, Taylor 10-2-32-1 (w-1), Campbelle 1-0-7-0 (w-1), Quintyne 6-0-33-1 (w-1), Dottin 5-0-24-1 (w-2), Kyshona Knight 2-0-19-0 (w-1, nb-1).
WEST INDIES innings
Kycia Knight c & b van Niekerk 46
N. McLean c wkp. Chetty b Benade 5
S. Taylor c Ismail b van Niekerk 75
Kyshona Knight c wkp. Chetty b Kapp 4
D. Dottin c Letsoalo b Loubser 24
S. Campbelle c Fritz b Kapp 33
M. Aguilleira c Letsoalo b van Niekerk 9
S. Quintyne c Letsoalo b Ismail 9
T. Smartt not out 0
S. Daley not out 4
Extras (lb-7, w-18) 25
Total: (8 wkts, 45.3 overs) 234
Fall of wickets: 1-15 (McLean), 2-141 (Kycia Knight), 3-146 (Taylor), 4-173 (Dottin), 5-173 (Kyshona Knight), 6-196 (Aguilleira), 7-225 (Quintyne), 8-230 (Campbelle).
Bowling: Kapp 8.3-2-42-2 (w-5), Benade 7-1-53-1 (w-5), Ismail 9-2-35-1, Letsoalo 2-0-14-0 (w-1), van Niekerk 9-0-47-3 (w-1), Loubser 10-036-1 (w-1).
Points: West Indies Women 2, South Africa Women 0.