The eighth-seeded Anisimova reached her second major final in a row after rallying to overcome Osaka 6-7 (4/7), 7-6 (7/3), 6-3 in a match that stretched well past midnight in New York.
"I wasn't sure I would make it past the finish line. I tried to dig deep. It was a huge fight out there," said Anisimova.
"It means the world. I'm trying to process that right now, it's a dream come true. The hope is to be the champion but I'm in the final now and I'm excited."
Osaka, seeded 23rd, was enjoying her best Grand Slam run since winning her second Australian Open title in 2021 - the last of her four major crowns.
She looked on course to go a step further after taking the first set in a tie-break, boasting a 26-1 record at this level when doing so.
Four breaks in six games to begin the second set betrayed the nerves on both sides.
Anisimova broke for third time to go 5-4 up, but as in the previous two instances then lost her own serve, double-faulting to keep Osaka in the set.
In a reversal of the first tie-break, Anisimova took charge of the second to level the contest.
Anisimova carried that momentum into the decider and broke for a 3-1 cushion as she continued to punish Osaka's ineffective second serve.
Two comfortable service games moved Anisimova 5-2 clear. Osaka held before the American earned two match points in a dramatic final game.
Osaka saved both and carved out two break points only for Anisimova to cut short the comeback and secure victory at the third attempt.