Sri Lanka entered the final day 347 runs behind the West Indies after trailing by 376 when the home team declared its second innings on Thursday at 280-4.
The experienced opener scored a patient 85 which, along with half-centuries from Kyle Mayers and Jason Holder, allowed West Indies to declare at 280/4.
Dinesh Chandimal and Dhananjaya de Silva put in an unbroken fourth-wicket partnership of 59 as Sri Lanka end the day at 136-3, 218 runs behind.
The West Indies captain's stands of 71 with Kyle Mayers, 51 with Holder, and an unbeaten 65 with Rakheem Cornwall ensured they finished the first day on top
When stumps were drawn early, the West Indies were 236-4, with Bonner 113 not out and Jason Holder on 13.
Starting 102 runs behind on the first innings, Sri Lanka reached 476 in its second innings for a lead of 374.
Cornwall was 60 not out at stumps, the first Antiguan to score a Test half-century at the Sir Vivian Richards Stadium.
Holder's spell broke the back of the innings and he then ripped through the lower half of the batting.
The Windies new Test captain celebrated his first Test in charge against Sri Lanka as he ran out Oshada Fernandes with a direct him as former skipper Jason Holder picks five-for.
Gunathilaka has been reprimanded for breaching Level 1 of the ICC Code of Conduct during the same match for giving a send-off to Nicholas Pooran.
The victory also gave West Indies 30 valuable points and moved them up to sixth position in the International Cricket Council's Super League table in the run for the 2023 World Cup.
The third and final ODI played in Antigua was briefly halted during the 38th over of the first innings when a swarm of bees forced players to lie down on the ground.
Holder, who has been replaced as captain by Kraigg Brathwaite for the Test series, missed the tour of Bangladesh along with batsman Darren Bravo, who too returns to the squad.
Lewis made 103 and Hope 84 to set the strong foundation that allowed the West Indies to overtake Sri Lanka’s 273-8 with two balls to spare.
Danushka Gunathilaka was adjudged out for obstructing the field during the 1st ODI against Sri Lanka, but the replays suggested that it might not have been deliberate from the batsman.
The West Indies chased the 233-run target with Shai Hope making 110 and his opening partner Evin Lewis adding 65.
Fabian Allen hit three mighty sixes in the 19th over to help the West Indies to a series-clinching three-wicket win over Sri Lanka in the third T20I.
In Perera's absence, Danushka Gunathilaka was called in to open the batting for Sri Lanka in their second innings.
Sri Lanka captain Suranga Lakmal and Lahiru Kumara took three wickets each as the Windies squandered their opportunity to bat the tourists out of the game.
Meanwhile, Chandimal faces a lengthy ban after having admitted to the more serious Level three offence which relates to 'conduct that is contrary to the spirit of the game.'
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