The 20-year-old Anisimova, a surprise semifinalist at Roland Garros three years ago, has now beaten Osaka in back-to-back grand slams after her third-round victory at the Australian Open in January.
In their latest clash at Roland Garros — arguably the pick of the first-round matches in the women’s draw — a close, seesawing first set featured five breaks of serve, including the first three games of the match.
Anisimova seized the advantage when she broke Osaka at 5-5 and went on to take the first set in 48 minutes, while in the second, she broke at 3-3 and twice held serve to wrap up the win.
The American, ranked No. 27 in the world, will face Croatia’s Donna Vekic in the second round on Wednesday.
“When you see Naomi Osaka in the first round, you don’t think it’s going to be easy,” Anismiova said in her on-court interview after the game.
“It was a very tough match. I was going out there and I knew I had to play good tennis … I’m just very happy to be back here and through the first round.”
Osaka withdrew from last year’s French Open having declined to speak to the media in order to protect her mental health.
On Friday ahead of her first-round game, Osaka spoke to the media and admitted she was “still thinking about” the events at last year’s tournament.
The defeat to Anisimova means Osaka ends her clay-court swing having played just three games: she lost in the second round of the Madrid Open and had to withdraw from the Italian Open due to an ankle injury.
Last week, the men’s and women’s professional tours, along with the International Tennis Federation (ITF), announced that ranking points would not be awarded at Wimbledon following the move to exclude Russian and Belarusian players from this year’s event amid the war in Ukraine.
“I’m the type of player that gets motivated by seeing my ranking go up or stuff like that,” Osaka told reporters on Monday.
“I think the intention is really good but the execution is kind of all over the place.”
Swiatek moves on, Krejcikova crashes out
Elsewhere in the women’s draw, 2020 champion and world No. 1 Iga Swiatek comfortably progressed to the second round with a 6-2 6-0 win against Lesia Tsurenko.
The victory extended Swiatek’s unbeaten run to 29 matches — the longest on the WTA Tour since 2013.
Meanwhile, last year’s champion Barbora Krejcikova suffered an early exit with a shock 6-1 2-6 3-6 defeat against teenager Diane Parry.
Buoyed by the support of a home crowd, Parry recovered from early breaks at the start of the second and third sets — which included winning six-straight games in the second — to take her first ever victory against a top-10 player.