After spinners Moeen Ali and Adil Rashid restricted the visitors to 288-6, Bairstow completed his century from 90 balls having shared an opening stand of 156 with Roy.
With Joe Root contributing 46, England secured their 11th win of their last 13 completed matches.
Bairstow's knock, which included 17 fours, was the highest by an England player against West Indies in one dayers, eclipsing Marcus Trescothick's 130 in 2004.
Roy, who was drafted in for the last two one-dayers to replace Hales, made the most of his recall as he scored his second successive fifty.
Roy notched up 11 fours and a six as a rampant England raced to 100 runs within 15 overs before he was dismissed lbw by pace bowler Miguel Cummins just four short of a century.
Root belted a six down the ground to secure victory as England finished on 294 for one with 12 overs remaining.
"I'm pretty pleased. It's nice to finish a long summer with some runs and head into the winter with confidence. You wait a long time for a first hundred and when it comes you want to capitalise," said man-of-the-match Bairstow.
(Reporting by Pritha Sarkar, editing by Toby Davis)
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