Sunil made his debut in first-class cricket for Trinidad and Tobago in February 2009 during the Regional Four Day Competition, bowling thirteen overs without taking a wicket. He did not play another first-class match until nearly a year later, and after going wicketless in the first innings claimed a single scalp in the second, that of tail-ender Lionel Baker.

On 19 January 2011, during the Caribbean Twenty20, Narine played his first Twenty20 (T20) match but did not bowl as the match was rained off before Trinidad and Tobago could bowl. T&T won the competition and Narine managed five wickets at an average of 13.40. By virtue of winning the competition Trinidad and Tobago qualified for the 2011 Champions League Twenty20 held in September and October, in which Narine was one of three bowlers to take ten or more wickets. He made his List A debut on 20 October 2011 in the Regional Super50, claiming figures of one wicket for 35 runs (1/35); his wicket that of opening batsman Miles Bascombe. Trinidad and Tobago won the competition and Narine was the leading wicket-taker in the competition with 15 scalps, five more than the nearest competitor, fellow spin bowler Nikita Miller.

Narine is the all-time leading wicket taker in Champions League T20 history with 39 scalps.

In May 2018, he was named as one of the ten marquee players for the first edition of the Global T20 Canada cricket tournament. On 3 June 2018, he was selected to play for the Montreal Tigers in the players' draft for the inaugural edition of the tournament.

When the West Indies toured India in November and December 2011 Narine was included in the squad. He made his One Day International debut in the third fixture on 6 December, taking the wickets of Virat Kohli and then Ravichandran Ashwin to help the West Indies to a 16-run victory. Playing in the final two matches (both won by India) Narine took one more wicket while conceding a further 87 runs.

Back in the Caribbean, Narine played three of T&T's six matches in February 2012 in the Regional Four Day Competition, taking 31 wickets at an average of 9.61, and finishing as the team's leading wicket-taker and seventh overall. Australia arrived in the West Indies in March, and their tour began with five ODIs. Narine and West Indies fast bowler Kemar Roach each finished with eleven wickets and were joined leading wicket takers in the series which was drawn 3–3 .^[20][21]

Following