Badosa was overwhelmed by Qinwen Zheng, the 19-year-old rapid improver from China, 6-3, 6-2. Qinwen won 10 of the last 12 games, playing fearlessly on Badosa's serve to break her four times.
"It's not a surprise. I always knew I had the level, I just had to make it," Qinwen said after her first top-10 win.
Garcia was upset in the second round by another Chinese player, Zhang Shuai, who prevailed 4-6, 7-6 (5), 7-6 (5) in 2½ hours.
Garcia broke Zhang in the opening game and won the set with her 10th ace. But despite serving 27 aces -- beating Qinwen's mark of 21 in a match for best on tour this year -- Garcia couldn't hold her form and Zhang used her speed and precision to take the second set.
Zhang said her many years of playing and training in Japan paid off.
"I was trying to stay calm. I told myself in the tough moments how I never lose on this court so today I will win," she said. "This is my home tournament, so that gave me a lot of motivation. Everything is positive here, and that's why I played really well."
Rybakina was coming off losing a three-set final in Slovenia last weekend and struggled to find any rhythm against an in-form Liudmila Samsonova, who won their tournament opener 6-2, 6-4.
Samsonova won two tournaments in August and reached the fourth round of the US Open, and she was calmly efficient in Tokyo.
"I'm incredibly happy about this match," she said. "It's always tough to play Elena. She's a big champion now, so I was prepared for a big fight. Last month was very positive for me. Winning a tournament I have more confidence, but I have to stay focused."
She faces China's Xinyu Wang in the second round.