Bairstow's 68 from 40 balls set England on their way to a relatively comfortable win with seven balls to spare, aided by some poor bowling and fielding from West Indies, who dropped four catches.
England, who lost the three-match test series 2-1 in the Caribbean and drew a five-match ODI series 2-2, will look to wrap up a series win in St Kitts and Nevis on Friday.
(This story was refiled to fix typo in headline.)
(Reporting by Simon Evans; Editing by Toby Davis)
