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The team, bidding to become the first British crew to win the America's Cup, earn two points for the next phase, the qualifying series in May and June.
The winners of that will face Oracle Team USA in the main event, the 2017 America's Cup later in June.
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Ainslie's team won after a tie-break in the regatta in Japan by virtue of a better result in the last race.
Land Rover BAR finished the series with 512 points, 19 ahead of Oracle Team USA, the two-time defending America's Cup champions, in second place.
Emirates Team New Zealand, who lost an 8-1 lead to Oracle in the 2013 America's Cup, finished third overall with 493 points.
Ainslie, the most successful sailor in Olympic history, is attempting to end Britain's long wait to bring the America's Cup back to the UK, where the oldest trophy in international sport was first contested in 1851.
"It's a massive day for us, proving we can win at the top end. It's a big step towards the America's Cup next year in Bermuda," said Ainslie, who was part of the winning Oracle team three years ago.
"We are under no illusions over just how tough it is. We hope to have the fastest boat next year."
Land Rover BAR held a one-point advantage after the first day of the Fukuoka regatta but Artemis Racing of Sweden won the first two races on Sunday.
Ainslie's crew needed to finish ahead of the Swedes in the last race of the day to clinch the title and came in third, with Artemis one place further back.
Sir Ben Ainslie's Land Rover BAR team won the America's Cup World Series with a narrow Fukuoka regatta victory.