The Sox lose for just the third time this season (17-3).
Left-hander Manaea struck out 10 Red Sox batters in his career-best performance, which included two walks and a deal of controversy. Dallas Braden was the last Oakland pitcher to go the distance without allowing a hit when he tossed a flawless game in 2010.
The last no-hitter against Boston was by Seattle's Chris Bosio in 1993.
Initially Benintendi was called safe but the umpires conferenced on the field and it was ruled that the Red Sox runner illegally ran into foul territory to try and avoid the tag from Olson. Shortstop Marcus Semien dropped a popup in shallow center field earlier in the game, and Manaea assumed it was scored a base hit.
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Manaea (3-2) had been battered by Boston in three previous starts, going 1-2 with a 13.50 ERA.
An inning later, it again appeared that Manaea's no-hitter was over.
The A's starter walked Mookie Betts to start the game, making perfection impossible.
"I've caught a lot of great pitchers in this game", A's catcher Jonathan Lucroy said.
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Manaea said he tossed the Red Sox a mixture of fastballs in and out, changeups and sliders. "I have eight years in the (majors) and that was most well-pitched, well-executed game I've ever had behind the plate".
Despite complaints from the Red Sox, the history books will show a no-hitter by Manaea, and one that was well-deserved.
Of course, Benintendi and the Red Sox were none too pleased about it. "A stretch of silence filled the Coliseum while official scorekeeper Art Santo Domingo deciphered a proper ruling under significant circumstances.Semien was charged with an error, Leon was denied a hit, and Manaea maintained his flirtatious pursuit of history - achieved soon thereafter.Video: "BOS@OAK: "Leon reaches first on Semien's error" I know he's got it in him", Semien said. "It's a big-league hit and they don't grow on trees".
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