Jonny Bairstow struck a maiden one-day international hundred as England condemned West Indies to a seven-wicket defeat at Old Trafford on Tuesday that means the twice former champions can no longer gain direct entry to the 2019 World Cup.
West Indies, the 1975 and 1979 World Cup winners, had to take this five-match series 5-0 or 4-0 with a tie or no result if they were to avoid the indignity of a qualifying competition for the next edition in England in two years' time.
But a total of 204 for nine, in a series-opener reduced to 42 overs per side after a wet outfield delayed the start by two hours, never looked enough.
England finished on 210 for three, winning with a mammoth 67 balls to spare.
Bairstow, who justified his retention at the top of the order, was exactly 100 not out – his first century in 28 matches at this level coming six years after his ODI debut.
Ben Stokes, who ended the contest with a six off spinner Ashley Nurse, was 23 not out.
Test wicket-keeper Bairstow, who made 43 as an opener in England's last ODI – an eight-wicket Champions Trophy semi-final defeat by eventual winners Pakistan in Cardiff in June – kept his place at the top of the order instead of Jason Roy, who was out for a golden duck in West Indies' T20 victory in Durham on Saturday.
Bairstow was quickly into his stride, driving West Indies captain Jason Holder through the covers for the first of 11 fours in 97 balls.
Together with Yorkshire team-mate Joe Root he put on 125 in 19 overs for the second wicket before England's Test captain played-on to Kesrick Williams for 54.
But Bairstow, whose previous highest ODI score was a match-winning 83 not out against New Zealand in Durham two years ago, went to his century with a hard-run three off Nurse despite slipping.
His century came just over a month after Bairstow was out for 99 in an Old Trafford Test against South Africa.
"It seems a long time ago that I made my debut in ODI cricket," Bairstow told Sky Sports.
"When you get a chance you try to take it but with the strength in depth that we've got in the England side at the moment, the opportunities are few and far between."
He added: "We've got a serious belief within the side that, although we didn't do ourselves justice in the Champions Trophy, that going forward to the World Cup and the rest of this series we need to rectify that."
Earlier, West Indies innings in this day/night clash fell away after a breezy opening stand of 45 between Chris Gayle and Evin Lewis.
Stokes took three for 43 with only West Indies captain Jason Holder's 41 not out ensuring the tourists got past 200.
Holder's decision to bat first meant big-hitting opener Gayle was straight into the action for his first ODI since the 2015 World Cup following a dispute with Caribbean cricket chiefs.
Gayle should have been out for a third-ball duck when he edged a drive off Chris Woakes only for second slip Root to drop the catch.
Jamaica left-hander Gayle cashed in by driving David Willey for two sixes in an over.
But off-spinner Moeen Ali broke the opening stand when with just his third ball when Lewis pulled a long hop to Alex Hales at square leg.
West Indies were soon 53 for two when Gayle, whose 37 had come off just 27 balls including two fours and three sixes, skyed a drive off Woakes and Root, atoning for his earlier error, held an excellent catch over his shoulder running back.
Bairstow, playing as a specialist batsman in this match, then held a leaping catch at deep midwicket to dismiss dangerman Shai Hope (35).
West Indies, who failed to qualify for this year's Champions Trophy tournament in England, continued to struggle before Holder hit out.
The series continues at Trent Bridge on Thursday.