England's openers shared a century stand for the second time in successive ODIs for the Alexander Edler Youth Jersey first time since Nick Knight and Marcus Trescothick did so in 2003.
Roy also compiled his second consecutive fifty after replacing Alex Hales - not considered for selection following the incident outside a Bristol nightclub which also involved Ben Stokes - at the top of the order.
Roy endured a difficult start to the summer in the Champions Trophy and paid the price www.indianapoliscoltsauthorizedstore.com/al-woods-jersey when he was dropped in favour of Bairstow, but has made the most of his recall.
He found the boundary with ease, stroking 11 fours and a six in his innings, but just as impressive was his understanding with Bairstow as the pair regularly converted obvious singles into twos.
England raced to 71 from the first 10 overs, and to 100 within 15, before Roy departed four short of his century.
In what was a chanceless innings, Bairstow registered the highest score by an Englishman against West Indies in ODIs, beating the 130 by Trescothick in 2004.
Root completed the run-chase with a six down the ground and in doing so became the third-fastest Braxton Miller Jersey player to reach 4,000 ODI runs, in his 91st innings.
Only Hashim Amla (81) and Viv Richards (88) have reached the milestone quicker than the England Test captain.On the latest date in the year an international has been played in the United Kingdom, Chris Gayle got the tourists off to a flying start.
The opener, in what may be his last international appearance in England, scored 40 from 29 balls.
Gayle caused problems for Jake Ball, hitting the seamer for 34 off six consecutive balls across two overs, before he was dismissed by a slower ball from debutant Tom Curran.
Ball, who is in England's Ashes squad, finished with figures of 1-94 off 10 overs - the third worst by an England www.newyorkjetsauthorizedstore.com/brent-qvale-jersey bowler in an ODI.
After the explosive start by West Indies, England's spin duo of Moeen (1-36) and Rashid (1-42) worked in tandem to restrict the flow of runs, with the Windies failing to find the boundary between the 10th and 31st overs.
Each batsman in West Indies' top eight reached double figures, with Shai Hope scoring 72 and debutant Sunil Ambris (38 off 27) and Ashley Nurse (31 off 12) accelerating the innings late on, but the tourists were short of a score to trouble the hosts.
They finish the tour having also lost the Test series 2-1, but were victorious in the sole Twenty20.