The English team’s victory has squared the series at 1-1. Set a formidable target of 329 to keep the three-match series alive, Livingstone cracked an unbeaten 124 off 85 balls including nine sixes as England timed their chase to perfection.
West Indies looked favourites after harvesting 93 off the final 10 overs of their innings in which Shai Hope struck a superb 117 and England tried nine different bowlers.
England had little margin for error at 160-4 after 28 overs but Livingstone, in partnership with Sam Curran who made a run-a-ball 52, kept them on track, although 100 off the last 10 overs for victory was still a sizeable task.
Also read: Late Malard goal gives Man United 1-1 WSL draw vs Arsenal
The pendulum swung rapidly towards the tourists though as Livingstone turned up the heat with some huge sixes off some poor West Indies bowling in his first ODI century.
In the end it was comfortable for England as Livingstone hit 22 runs off Shamar Joseph in the 47th over to make victory a formality. He scored the winning run with 15 balls to spare.
England’s innings was given some impetus by opener Phil Salt who made 59 off 59 balls while Jacob Bethell scored 55.
"We needed somebody in our top six to go on and get us a big score. Salty batted beautifully, put the pressure on them," Livingstone said. "We were sloppy in the field but our bowlers did well, took wickets throughout.
"We have got a lot of young guys learning the ropes in international cricket, this will do them a world of good. Back in the series, looking forward to Barbados."
"DECENT SCORE"
West Indies captain Hope, who bagged his 17th ODI century, said he felt his side had control.
"Personally I thought it was a decent score, especially with the conditions, the outfield was heavy, the surface was up and down, but it was not enough," he said.
Also read: Irfan Khan, Saim Ayub to make debut in first ODI against Australia
"We thought we had clear plans, but we did not execute our plans well today. We gave them a lot of easy options to score and when you play international cricket, the guys will capitalise and that s what happened."
Hope arrived at the start of the fourth over after West Indies openers Brandon King and Evin Lewis both fell cheaply to John Turner after the hosts were invited to bat first.
He and Keacy Carty steadied the ship in a stand of 143 before Carty, who was dropped on single figures, was out for 71, bowled through the gate by Adil Rashid.
Hope was dropped on 60 off the bowling of Bethell and he took full advantage against a ragged England attack.
With Hope set, Sherfane Rutherford piled pressure on England with a half century from 36 deliveries while Shimron Hetmyer s 24 came off 11 balls. Hope was eventually out when he mistimed a drive off Jofra Archer and picked out Livingstone.
When Matthew Forde cleared the boundary rope three times in the 50th over it looked bleak for England.
The tourists lost opener Will Jacks for 12 as he struck a Forde delivery straight to Lewis at deep square leg.
Jordan Cox looked uncomfortable before falling to a short-pitched ball from Shamar Joseph but Salt showed great control to reach his half century before becoming Forde s second victim.
Livingstone, first with Bethell and then with Curran, was the difference between the sides, though, as he punished some wayward West Indies bowling.