Sri Lanka, who chose to bat first, laboured through their innings after decent starts from their top batsmen set them on an optimistic path.
But the bowlers contained the run flow especially medium-pacer Selman who finished with a miserly 10-5-8-2.
Front line batters Deepika Rasangika top-scored with 28 and Chamari Jayangani got 27 as the home side reached 105 for the four.
A lower-order collapse saw the Sri Lankans sinking to 127 for 8 and appeared headed for a small total.
However, a late rally from Sripali Weerakkody and Dilani Manodara resulted in a 34-run partnership that restored some respectability to the score.
West Indies, on the strength of a 41-run opening partnership between Natasha McLean and Juliana Nero, were cruising to victory despite losing a few wickets towards the end.
McLean was dismissed for 17 while Stafanie Taylor, in her first match as captain, fell cheaply to the medium pace of Chamani Seneviratna.
West Indies, however, were in a spot of bother as Nero fell for 30 with the score on 76.
The driving force behind the Windies chase emanated from a 73-run, fourth-wicket partnership between Deandra Dottin and Kyshona Knight.
Dottin hit two fours and four sixes to score 43 off 39 balls while Kyshona’s knock of 36 from 54 balls was more composed.
The Caribbean side stumbled towards the end as Knight and Dottin were dismissed in consecutive overs.
SRI LANKA WOMEN
C. Kumarihami c Kyshona Knight b Selman 16
P. Weerakkody lbw b Selman 13
C. Jayangani run-out 27
D. Rasangika c Campbelle b Mohammed 28
S. Siriwardene c Taylor b Campbelle 7
S. Dolawatte run-out 8
E. Kaushalya c Mohammed b Smartt 2
C. Seneviratna b Campbelle 1
S. Weerakkody stp. Kycia Knight b Taylor 21
D. Surangika not out 14
I. Ranaweera not out 2
Extras: (b-4, lb-5, w-13, nb-3) 25
Total: (9 wkts, 50 overs) 164
Fall of wickets: 1-31 (Kumarihami), 2-39 (P- Weerakkody), 3-85 (Rasangika), 4-105 (Siriwardene), 5-107 (Jayangani), 6-113 (Kaushalya), 7-117 (Seneviratna), 8-127 (Dolawatte), 9-161 (S. Weerakkody).
Bowling: Selman 10-5-8-2 (w-1), Munroe 5-1-21-0 (w-3), Smartt 10-1-30-1 (nb-3), Mohammed 9-0-48-1 (w-3), Taylor 10-1-26-1, Campbelle 5-0-13-2 (w-5), Kyshona Knight 1-0-9-0 (w-1).
WEST INDIES WOMEN
N. McLean lbw b Seneviratna 17
J. Nero c Rasangika b Siriwardene 30
S. Taylor c wkp. P. Weerakkody b Seneviratna 7
Kyshona Knight stp. P. Weerakkody b Siriwardene 36
D. Dottin c Surangika b Ranaweera 43
Kycia Knight not out 13
S. Campbelle run-out 1
A. Mohammed not out 0
Extras: (lb-5, w-13) 18
Total: (6 wkts, 38 overs) 165
Fall of wickets: 1-41 (McLean), 2-58 (Taylor), 3-76 (Nero), 4-149 (Kyshona Knight), 5-149 (Dottin), 6-163 (Campbelle).
Bowling: Kaushalya 4-0-21-0 (w-2), S Weerakkody 5-0-27-0 (w-2), Seneviratna 10-2-23-2, Ranaweera 8-1-31-1 (w-1), Siriwardene 9-1-41-2 (w-6), Dolawatte 1-0-9-0, Kumarihami 1-0-8-0.