Man of the Match Bravo scored 102 and shared in two crucial partnerships - a 109-run third-wicket partnership with Hope, who made 64, and a fourth-wicket partnership with Pollard that set up the West Indies for a third consecutive victory. The captain remained unbeaten on 53 at the end.
Chasing 275, after Sri Lanka made 274 for 6, their best score of the series, the West Indies had their worse start of the series. After stands of 143 and 192, respectively, in the first two matches, Evin Lewis and Hope managed only 24 runs on this occasion.
Lewis, who has been in ominous form with scores of 65 and 103 in the two previous matches, was bowled by Suranga Lakmal for 13 at the end of the fifth over. The West Indies crawled to 39 for 1 in the 10th over when Jason Mohammed was bowled by Wanindu Hasaranga de Silva, who was getting his first wicket of the ODI series.
His dismissal brought Hope and Bravo together for the first of the two instrumental partnerships of the West Indies innings. However, after keeping the scoreboard ticking over at close to five runs an over, the pair got bogged down by the tight bowling. By the start of the 32nd over the pair had taken the score to 148 when Hope got out trying to slog Thisara Perera first ball only be caught by Suranga Lakmal running in from long-on.
Hope had made 64, his third consecutive score of 50 or more in the series and on the sixth consecutive occasion overall. Nicholas Pooran came intending to push the score along hitting two sixes in what was to be a brief stay at the crease. Three overs later he was back in the pavilion out lbw to Danuska Gunathilaka for 15 to leave the West Indies in a spot of bother at 169 for 3, still needing 106 from 78 balls.
Pollard arrived at the crease intent on pushing the scoring rate without unnecessary risk. He knocked balls into the gaps, running singles and twos, sprinkling four fours in between. Bravo soon followed suit and together they put on 80 runs while bringing the run rate down from near eight an over to near six and which took the West Indies within sight of their target.
By the time Bravo got out trying to hit Lakmal over extra cover, the West Indies needed 25 from 23 balls. Bravo hit five fours and four sixes.
Holder joined Pollard and together began a steady run toward the required runs.
Pollard hit one six in his 42-ball innings and it was perhaps the most important one of the innings.
It came from the last ball of the 48th over bowled by Asitha Fernando that yielded 14 runs, resulting in the West Indies needing nine from 12 balls.
After missing with an almighty swipe from the first ball of the 49th over bowled by Lakmal, Jason Holder finished the job hitting a four and a six off the next two balls to finish the job unbeaten on 14.
Lakmal, who gave up the winning runs, finished with 2-56 from 9.3 overs.
Earlier, Sri Lanka, who had been put in to bat, only managed their competitive score of 274 for 6, due to an unbroken seventh-wicket stand of 123 from 111 balls between Hasaranga and Ashen Bandara.
Hasaranga who should have been run out for 42, hit seven fours and three sixes on his way to his best ODI score of 80 that came off just 60 balls while Bandara was unbeaten on 55 that included three fours and six.
They had taken the score from 151 for 6 sliding from 68 without loss.
Gunathilaka made 36 before he lost his wicket to Alzarri Joseph. Seven balls later and two balls later Dimuth Karunaratne was bowled by Mohammed for 31. It was the start of a trend wherein the Sri Lankan batsmen would all get starts and then got out.
Akeal Hossein took 3-33 taking the wickets of Pathum Nissanka for 24, Dinesh Chandimal for 16 and Dashun Sanaka for 24. The latter two getting out in a similar fashion playing across the line to faster straight deliveries and getting bowled.
By that time, Sri Lanka was struggling at 143 for 5 in the 31st over.
When Perera was run out by a direct hit from Nicholas Pooran seven balls later, Sri Lanka was slipping fast at 151 for 6 before Hasaranga and Bandara pulled out their rescue act.
For his scores of 102, 84 and 64, Shai Hope was named Player of the Series.
Both teams will now turn their attention to the Test series that begins on March 21.