The 18-year-old Andreeva had opened her repeat bid with an imperious 6-0, 6-0 demolition of Solana Sierra.
But she was in trouble early and often against 44th-ranked Siniakova in a rollercoaster contest that ended with a shot from Siniakova that hit the net cord and dribbled over in one last frustrating moment.
The 18-year-old Russian slung her racquet as she approached the net before departing the court with a defiant gesture at the censorious crowd.
Siniakova, a former doubles number one, admitted it was an awkward way to seal the win in a match that featured seven service breaks for each player and 43 break chances between them.
"Of course, I'm happy it went on the other side," she said. "I was, like, should I cheer? It's a really tricky finish. But definitely I will not say I'm not happy."
Siniakova said the swirling winds on Stadium Court were troubling both players.
Andreeva's emotions had already boiled over when she sailed a swinging volley long to surrender the second set, during which each player had remarks for the chair umpire about her opponent.
She regrouped to break Siniakova for a 3-2 lead in the third, but Siniakova won the next four games, saving two break points in the final game before gaining the win on her first match point.
Siniakova will face Elina Svitolina for a place in the quarter-finals after the ninth-seeded Ukrainian beat American Ashlyn Krueger 6-4, 6-2.
Djokovic takes down Kovacevic
Third seed Novak Djokovic overcame a second-set reverse to beat American Aleksandar Kovacevic 6-4, 1-6, 6-4 at Indian Wells on Monday and reach the last 16 for the first time since 2017.
The 24-time Grand Slam champion, who has won a record-equalling five titles at the California desert event, won the first set but was taken apart in the second before asserting his authority to seal victory in two hours and two minutes.
"Great performance from Alex," Djokovic said. "We know each other, we speak the same language, obviously, his whole family is Serbian. He's one of the best talents we have out there, particularly, one-handed backhand and, you know, it's very rare nowadays, and he's played a great tournament so far.
"Today I knew if he serves well and if he picks his spot in the box, it's going to be hard to break. That's what happened, actually. I mean, he was serving extremely well," the 38-year-old added.
"I knew coming into the match that if he serves well and if he picks his spot in the box, it's going to be tough to break him," Djokovic said.
"I wasn't maybe feeling my rhythm on that return very well today, but he was just making my life very difficult, returning the serve.
"He was just acing me all over, getting a lot of free points.
"Today was really anybody's game until the last couple of points. That last game in the third, where he missed some first serves, gave me looks on the second, and I used it. That's pretty much it."
With five Indian Wells titles, Djokovic is tied for the record with Swiss great Roger Federer.
But the Serbian superstar hasn't made it to the quarter-finals in the California desert since his last title run in 2016, and now he's had to come through a pair of three-setters to return to the last 16.
Men's matches
He'll face defending champion Jack Draper for a place in the quarter-finals after the Briton beat Argentina's Francisco Cerundolo 6-1, 7-5.
Draper's victory here last year - featuring a semi-final win over Carlos Alcaraz - launched his rise to fourth in the world. But he then missed the better part of six months with an arm injury and arrived in California ranked 14th, his win over Cerundolo marking the first time since June that he's posted back-to-back ATP victories.
Cerundolo served for the second set at 5-4, but a few mistakes gave Draper an opening, and the Briton broke back, saving a pair of break points in the next game before finishing it off on Cerundolo's serve.
A pair of top-10 seeds were sent packing as Britain's Cameron Norrie ousted eighth-ranked Australian Alex de Minaur 6-4, 6-4 and Aussie qualifier Rinki Hijikata 10th-ranked Alexander Bublik 6-7 (3/7), 7-6 (7/3), 6-3.
Hijikata, ranked 117th in the world, claimed his first win over a top-10 player to advance to a meeting with Norrie in what is the biggest win of his entire career.
Women's matches
There was no drama for world number two Iga Swiatek, who defeated Greece's Maria Sakkari 6-3, 6-2.
Poland's Swiatek beat Sakkari in the final to claim both of her Indian Wells titles, in 2022 and 2024, but Sakkari had won their most recent encounter in the quarter-finals of the Qatar Open last month.
Swiatek said she had learned from "obvious mistakes" she made in Doha.
"I knew what to focus on today and I did that from the beginning till the end," she said. "So I'm really happy with my focus and the way I was prepared."
Swiatek next faces Doha champion Karolina Muchova, who blew past Antonia Ruzic 6-0, 6-3.
Meanwhile, earlier in the day, fifth seed Jessica Pegula demonstrated her resilience by recovering to defeat Jelena Ostapenko 4-6, 6-3, 6-2 and book her place in the fourth round.
The American dropped the opening set to the hard-hitting Latvian and former French Open champion before finding her range to take the next two sets and seal a hard-fought victory.