Chasing a modest 213 for victory, Root and Jonny Bairstow shared an opening partnership of 95. After Bairstow fell for 45, Root and Chris Woakes added 104 for the second wicket.
Woakes, promoted up the order due to injuries, departed for 40 but Root and Ben Stokes took the hosts and tournament favorites to their target with more than 16 overs to spare.
England’s third victory in four matches lifted them to second in the 10-team standings while West Indies are sixth following their second loss
In the first inning, England lost two fielders and dropped two outfield catches yet managed to dismiss the West Indies for 212 in 44.4 overs on Friday in cold, mainly overcast conditions in the 19th fixture of the World Cup.
Joe Root picked up his first two wickets in one-day international cricket since January 2018, both caught-and-bowled, and Barbados-born paceman Jofra Archer (3-30) picked up his first wickets against West Indies.
Archer was expensive in his opening spell but had a chance for a hat trick in his second, picking up his first wicket on a referral to the TV umpire when Nicholas Pooran (63) got a fine edge off his glove to England wicketkeeper Jos Buttler.
Archer trapped Sheldon Cottrell lbw on the next delivery and later got his third when he had Carlos Brathwaite (14) caught behind with a ball that brushed the batsman’s shoulder.
Mark Wood (3-18) finished off the innings when he bowled Shannon Gabriel with a yorker as the last four West Indies wickets fell for 10 runs.
The late collapse started the ball after England captain Eoin Morgan hobbled from the field after having back muscle spasms in the 40th over, when West Indies was 202-6 and before Archer had taken a wicket.
Making matters worse for England, Morgan was the second batsman to hobble off the field in the first innings. Big-hitting opener Jason Roy strained his left hamstring in the eighth over and didn’t return to the field.
Roy wasn’t allowed to bat any higher than number seven as England chased 213 to win. The two dropped outfield catches weren’t too damaging for England. Gayle was on 15 when Wood dropped him in the outfield. Gayle went on to set the career record for most runs in ODI between West Indies and England before he was finally caught on the boundary for 36.
Andre Russell was on three when he was dropped in the outfield by Chris Woakes. He clubbed a pair of sixes in the same over from Adil Rashid but was eventually out for 21, caught by Woakes off Wood’s bowling.
Woakes (1-16) caused trouble early for the West Indies after England won the toss and elected to field. He took the first wicket in the third over and had Gayle dropped by Wood at third man when the West Indies star was on 15.
Gayle shared a 50-run second-wicket stand with Shai Hope (11) and surpassed Viv Richards’ record of 1,619 career runs in ODIs against England when he stroked Woakes for a boundary. He drove the next ball down the ground for six just for good measure. But he was out for 36 from 41 balls setting the bilateral run record at 1,632 when he pulled Liam Plunkett into the deep and Jonny Bairstow took a running catch.
Hope was out two balls later, forcing the West Indies to rally around an 89-run fourth-wicket stand between Pooran and Shimron Hetmyer (39).
Part-timer Root picked up a pair of return catches to remove Hetmyer and Jason Holder (9) and return 2-27, and Archer cleaned up the tailenders.
Top-ranked England entered the game with two wins and a loss, and West Indies had a win, a loss and a point from a washed out match against South Africa.