In the day's other match, Sophie Devine sizzled with both bat and ball to help New Zealand defeat South Africa by 22 runs. Devine scored 59 off 46 balls and then picked up two wickets.
Chasing a revised target of 48 in a rain-affected match, West Indies were restricted to 42 for eight in as many overs at the Galle International Stadium.
Needing 12 off 12 with six wickets in hand, Chamani Seneviratna had Juliana Nero stumped off the second ball of the penultimate over.
Two more wickets in the same over and the Sri Lankans were back in the game. In the last over another run-out, the fourth of the West Indies innings, sealed the match in Sri Lanka's favour.
The West Indians were earlier well on their way, scoring nine runs in the opening over. Last match's top-scorer Deandra Dottin's presence was reassuring for West Indies but Though Inoka Ranaweera's double-strike in the third over injected life into the game.
In a match reduced to 17-overs a side after wet outfield had delayed the start by an hour, Sri Lanka, after being asked to bat, made a good start scoring 21 off three overs.
However, the loss of their openers in successive overs slowed them down.
The rains came again and Sri Lanka's innings was halted at 50 for three after 10.3 overs, resulting in West Indies getting a revised target of 48.
