Narine had an instant impact when he came on in the 18th over, removing the prolific and experienced pair of Mahela Jayawardene (52) and Kumar Sangakkara (17) in his first three overs to immediately put the brake on what had been a promising start by the Sri Lankans.
Jayawardene was at his fluent best, dominating an opening partnership of 62 with Upul Tharanga before they were separated by West Indies captain Dwayne Bravo.
By contrast, Sangakkara never really got going and the West Indies were understandably delighted when he pushed a straightforward catch to Kieron Pollard at cover.
Ravi Rampaul backed up the frontline spinner's effort with three wickets and it was left to Sri Lankan captain Angelo Mathews to hold the innings together following the demise of the two big hitters.
His unbeaten 55 turned out to be the Sri Lankans' top score as he capitalised on an early bit of luck when put down by Chris Gayle off the bowling of pacer Kemar Roach.
All the bowlers were hard to get away on a sluggish surface, former ODI captain Darren Sammy being the most economical in a full ten-over spell, conceding 34 runs, while Marlon Samuels accounted for Dinesh Chandimal in giving up just 11 runs off four overs.
West Indies may fancy their chances of reaching what appears, on paper, a modest target, but will still be mindful of the threat posed both by Sri Lanka's varied bowling attack and a weather forecast that has not ruled out the possibility of an afternoon shower.
World Cup and Champions Trophy holders India are the third team in the tournament and they enter the fray on Sunday against the hosts.