England, who scored 226-6, claimed an unbeatable 2-0 lead in the three-match series. They beat the hosts by 45 runs at the same Vivian Richards Stadium on Friday in the opening encounter.
Root played a typically flawless innings to carry England home with 10 balls to spare as he and Woakes stemmed a mid-order slump with an unbroken 102-run partnership for the seventh wicket.
Woakes survived being dropped twice to score 68 as both teams used the brief series to prepare for June’s Champions Trophy.
West Indies, who won the toss and chose to bat, never got going on a slow pitch and were dismissed for 225 with 13 balls left of their 50 overs.
Jason Mohammed, who top scored with 50, featured in a 72-run partnership for the fourth wicket with Kraigg Brathwaite, who contributed a slow 42 off 70 balls.
Jonathan Carter offered a brief cameo with 39 off 36 balls but was deceived by a slow ball and lofted a catch off Liam Plunkett, who took 3-32.
England captain Eoin Morgan’s decision to ask Adil Rashid to bowl at the middle order proved to be a clever tactic as he took the wickets of the dangerous Jason Holder and Carlos Brathwaite.
England’s reply got off to a poor start as opener Sam Billings was caught behind for a duck in the first over.
Jason Roy might have perished in the next over but survived a lengthy review, given the benefit of the doubt after the Windies were convinced he had nicked one behind.
Roy went on to make 52 in a second wicket partnership of 86 with Root before his departure set off a mini collapse with five wickets falling for just 37 runs in 10 overs.
But Root kept the runs ticking over steadily as he and Woakes steadied the situation for England with Windies key bowler Shannon Gabriel bowling just three overs before suffering a side strain.
The last match in the series is being played at the Kensington Oval in Bridgetown, Barbados on Thursday.
