Sangakkara played a superb 95-ball unconquered innings, which was studded with six fours and one six, to help Sri Lanka post 219 for eight in the match, which was reduced to 41-overs a side after two rain interruptions last night.
Kemar Roach returned with an economical four-wicket haul but rest of the West Indies bowlers could not stop the run flow as Sri Lanka scored 159 in 22 overs after struggling at 60 for three in 19 overs on Sunday.
The visitors then returned to restrict West Indies to 190 in 41 overs, despite two fighting half-century by Lendl Simmons (67) and Darren Bravo (70), to keep themselves afloat for a place in the finals.
West Indies were set a revised target of 230 in 41 overs on the basis of Duckworth/Lewis scoring method but their runchase was derailed by the early top-order collapse which left them at 31 for four in 8.2 overs.
Shaminda Eranga and Lasith Malinga picked up three and two wickets each to contribute in Sri Lanka's win though West Indies did well to deny them a bonus point atleast.
With this win, Sri Lanka bagged four points to move to the top of the table with nine points from three matches but they are still not through to the finals as West Indies, despite the lose, too are on nine points from four games.
All eyes will now be on India's crucial ODI against Sri Lanka today as Mahendra Singh Dhoni's men not only have to beat Sri Lanka but also win big, considering that bonus points and net runrate will come into the calculation.
Earlier, Sangakkara ensured that Sri Lanka have a good score on board as he set the foundation early on and then accelerated in the end, despite losing partners at regular intervals.
Mathews (30) and Lahiru Thirimanne (23) were the other contributors for Sri Lanka in the match which was pushed to the reserve day after rain forced officials to call off the game yesterday.