Ali struck England's second-fastest ODI hundred off just 53 balls, with his second fifty coming in a world record 12 deliveries.
His 102 was the cornerstone of a total of 369 for nine -- England's highest in ODIs against West Indies.
Despite an impressive 94 from the returning Chris Gayle, it proved too much for the visitors to chase with England winning by the commanding margin of 124 runs on Sunday to go 2-0 up with two to play in this five-match series.
Ali hit eight sixes and Gayle six in a match featuring 28 in total, with both left-handed batsmen taking advantage of the short straight boundaries at southwest county Gloucestershire's headquarters.
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"I just had a slog really, and everything just seemed to come off," all-rounder Ali, known for being an elegant stroke-player, told reporters.
West Indies, who've now lost 14 of their last 15 completed ODIs against England, actually started impressively with the ball to restrict the home side to just 18 runs off the first five overs.
"We just didn't finish off well," said a rueful West Indies captain Jason Holder, who won the toss and fielded.
"They (England) bat deep. He (Ali) has played a special innings. I think we didn't execute our plans towards him.
One consolation for West Indies was the innings of Gayle, long one of the world's leading limited-overs batsmen.
He had marked his 38th birthday on Thursday by injuring his hamstring just before the toss while warming up and so missing a rainswept no-result in the second ODI at Trent Bridge.
- 'Surprising' Gayle -
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But the Jamaica opener was near his blistering best in Bristol.
"It was very special," said Holder of the veteran's 78- ball innings, which also featured nine fours.
"Not only did he get the start we wanted, he carried on and batted into the innings.
Meanwhile Holder insisted there was a far more thoughtful side to Gayle than might be apparent from a player who revels in a 'cool' image with the self-created nickname of the 'Universe Boss'.
"Chris is always a relaxed guy but, if you go to him, you'd be surprised by the amount of information you get from him," said Holder.
"I've been privy to having a few chats with him in the last couple of days and it's been wonderful."
This series has seen Gayle return to ODIs after a two- year dispute with Caribbean cricket chiefs and Barbados all- rounder Holder added: "He's shared a lot of information and helped me out a lot on the field.
Holder was adamant that West Indies, the World Twenty20 champions, were "not too far off" becoming a competitive side in the 50-over game.
"We just need to knuckle down a little more, especially when we bat," he explained ahead of Wednesday's fourth ODI at The Oval in London.
"'Death' bowling has obviously been a cause for concern in the recent past and we really need to tighten up there as well.