Root made 107 off 122 balls to help the tourists compile an imposing total of 303 for six after opener Moeen Ali had laid the foundations with 55 and wicketkeeper Jos Buttler added 99 late in the innings.
West Indies, in reply, were bowled out for 278 in the 48th over to concede the series 2-1 despite an heroic batting performance by Denesh Ramdin.
The home side were in early trouble after slumping to 43 for four in the eighth over when Ramdin came to the crease. The West Indian keeper proceeded to blast a career best 128 off 109 deliveries, pummelling 12 boundaries and five sixes.
His explosive innings threatened to turn the match around but the West Indian fightback ended when he was the last man out, bowled by a yorker from all-rounder Tim Bresnan (3-45) that knocked his leg stump out of the ground.
"We were confident to chase, it was a good wicket but the top order failed and it didn't quite come off at the end," West Indies captain Dwayne Bravo said at the post-match presentation.
"I think Root and Buttler batted well, they capitalised on the start they had... we didn't get it right at the key moments, the first 10 overs, it's something we have to work on, as a team and a batting group."
Root came out with England in a sticky situation at 37-2 after Ben Stokes went for a golden duck but calmly set about rebuilding the innings, whacking seven boundaries to reach his ton, despite being hit on the thumb.
Buttler was unlucky not to reach triple figures as well. He struck seven boundaries and four sixes only to fall in the last over when he misjudged a slower ball from Ravi Rampaul which he chipped in the air for a return catch.
"We thought we could hurt them if we got a partnership going, that's what Jos did at the end, once he got himself going - he looks unstoppable," England captain Stuart Broad said.
"We've taken some half chances, particularly in the last couple of games, and that yorker in the end shows it can work."
The teams will now play each other in three Twenty20s in Barbados, starting on Sunday.
- Sports & Recreation
- Jos Buttler
- Denesh Ramdin