Bairstow struck 141 not out as the hosts sealed the win with 12 overs to spare to complete a 4-0 series victory.
The tourists, seeking to end a long sequence of defeats against England, posted 288 for six despite becoming bogged down after a thrilling Chris Gayle cameo, but it never looked enough under the floodlights in the day-night encounter.
Openers Jason Roy and Bairstow started the home side's reply confidently, with Roy reaching his second consecutive half-century in the evening sunshine after his recall for the fourth match of the series, off 43 balls.
But his dismissal did little to upset England's rhythm. Joe Root batted smoothly while Bairstow steered a ball down to third man for a single to notch his second century of the series off 90 balls with 10 fours.
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The home side cantered past the winning post as Root finished alongside Bairstow on 46 not out, scoring the winning runs with a six.
- Gayle fireworks -
"I'm pretty pleased -- it's nice to finish a pretty long summer with some runs and head away this winter with some confidence," said Bairstow.
"The nature of sport means you have to bide your time if selection doesn't go your way and when you get an opportunity, try to take it."
Earlier, Gayle (40) lit up the gloom at the Ageas Bowl following a delayed start with a breathtaking brief knock under heavy late-September skies, hitting 34 runs off just six balls, all delivered by Jake Ball, including four successive sixes.
But as he threatened to take the game away from England, Liam Plunkett took a fine diving catch running backwards off a slower Tom Curran delivery and the West Indies lost all momentum.
Desperately needing to step up the scoring rate to post a competitive total, Shai Hope clubbed three successive fours off ODI debutant Curran but was caught on the boundary by Sam Billings off Ball for 72 off 95 balls.
Sunil Ambris (38 off 27 balls) and Ashley Nurse, with an impressive 31 off just 12 balls, gave much-needed impetus at the end of the innings as the West Indies went from 174-3 at the end of the 38th over to 288-6 at the end of the 50th over.
The formerly dominant West Indies, who will be forced to qualify for the 2019 World Cup, have now lost 16 of their past 17 completed ODIs against England and look a long way short of being able to compete on equal terms.
Curran replaced Chris Woakes in the England team while West Indies brought in Kyle Hope and debutant Ambris for the injured Evin Lewis and captain Jason Holder, who had to return home for a funeral.
England said the all-rounder would not be considered for selection by England "until further notice" following the emergence of a video apparently showing him fighting outside the club in the southwestern city of Bristol.
Test vice-captain Stokes was included in the Ashes squad announced Wednesday, despite reportedly injuring his hand in the incident that led to his arrest on suspicion of causing actual bodily harm.
The 26-year-old Durham all-rounder was released without charge on Monday but remains under investigation.