World number two Iga Swiatek, who lifted the prestigious trophy in 2022 and 2024, survived some sticky moments in a 6-0, 7-6 (2) victory over US qualifier Kayla Day.
Eighth-seeded Andreeva was understandably delighted with her performance against an opponent she'd never played before.
"I was pretty nervous because obviously I don't know what she's going to do," the 18-year-old Russian said. "Also the conditions were pretty tricky. The wind was changing directions every time. So I'm pretty happy with how I adjusted my game to these conditions."
The third-seeded Kazakh, who won the Indian Wells title in 2023, needed all of her patience and resolve in the face of an aggressive attack from Baptiste, but steadied herself in the final set to win 7-6 (5), 2-6, 6-2.
"It was a really tough match today, but I'm super-happy with the win," said Rybakina, who beat world number one Aryna Sabalenka to claim her second Grand Slam title in Melbourne in January.
After squandering an early break in the opening set, Rybakina fought off three set points to force the tie-breaker, in which three forehand winners put her in command before she pocketed the set with another.
But Rybakina was broken twice in the second set, Baptiste taking advantage to serve it out after Rybakina double-faulted on break point to hand the American a 5-2 lead.
A shaky service game from Baptiste gave Rybakina a break for a 3-1 lead in the third, and from there she was able to roll home.
"She played really well," Rybakina said. "She was staying aggressive. She has a good serve. I had my opportunities, didn't get them from the beginning, and then I was struggling in the second set, was rushing a bit.
"There are things for sure to improve on.
Drifting off
Swiatek sailed through her opening set against Day only for the 187th-ranked lefty to break the Polish star in the opening game of the second.
Swiatek battled back from 0-40 down to avoid falling 0-3, but when she fell behind 0-40 in the fifth game she couldn't escape and Day gained another break to lead 5-1.
Swiatek responded, winning five straight games as they went to the tiebreaker, in which she powered to a 5-0 lead.
"I think for sure I drifted off a little bit for some games, and then I became tight because of that," Swiatek said. "For sure I needed to get back to my first-set game.
"I feel like I did that quite well," added Swiatek, who is hoping a return to a venue she loves will kickstart a season in which she fell in the quarter-finals at the Australian Open and in Doha.
Fifth-seeded home favorite Jessica Pegula opened the night session on Stadium Court with a 4-6, 6-2, 6-3 win over Croatian veteran Donna Vekic.
Pegula is coming off a victory in Dubai, where she beat Elina Svitolina in the final to claim her fourth WTA 1000 crown.
Czech Karolina Muchova, winner last month in Doha, opened her campaign with a 7-5, 6-2 victory over Anna Bondar.