The 19-year-old Canadian triumphed in difficult, blustery conditions, overcoming Andreeva's tenacious defence and court coverage for the third top-10 win of her career. Andreeva served for the match in the final set, but was unable to get over the line, and exited the court in a flood of tears after two hours.
It was the second meeting between Andreeva and Mboko this season, a match the former won 6-3, 6-1 against a hampered opponent in the Adelaide final in January.
"It took everything, and at the end, we were both pretty tired. I'm glad to pull through today and get the win," Mboko said.
"It is my first time here, so far I am liking it a lot. I'm really excited to play here tomorrow."
Facing off at the first WTA 1000 event of the year, Mboko started sharply, asserting her authority from the off to rush to a 3-1 lead. However, Andreeva, 18, retrieved the break to restore parity at 3-3, before Mboko soared ahead to take the first set.
The second set saw both players struggling to hold serve, trading breaks in the wind before Andreeva crucially held at 5-3 to take it to a decider.
The pair were a lot more solid on serve in the third, but Andreeva pounced at the right time to lead 5-4. However, she was broken back after squandering a match point, as her mood began to sour.
Mboko took the initiative in the tiebreak, producing some stellar tennis. In the end, on the third time of asking, she completed the win with a gorgeous backhand winner.
She will face the winner of the match between Australian Open champion Elena Rybakina and Qinwen Zheng.
It is Mboko's second appearance in a WTA 1000 quarter-final, after she announced herself to the world in Montreal back in August, beating four-time Grand Slam champion Naomi Osaka to win the Canadian Open.
Swiatek moves through
Iga Swiatek survived a brief scare from Australia's Daria Kasatkina, battling from a set down to win 5-7, 6-1, 6-1, setting up a quarter-final with Maria Sakkari.
The top seed was well off her best in the opening exchanges, with the first set seeing five breaks of serve. Swiatek squandered a 5-3 lead as Kasatkina reeled off four straight games to go ahead.
Swiatek then fended off three break points at 1-1 in the second, but that proved to be the turning point, as the Pole went on to win the next seven games in a row, as well as 11 of the next 12.
The three-time champion has been a dominant force on these courts, reaching the quarter-finals for a fifth consecutive year.
Her last-eight opponent, Sakkari, sealed a first 1000 last-eight appearance since 2024, winning 7-6(3), 6-0 against qualifier Varvara Gracheva.
14th seed Karolina Muchova made her way safely through when fellow Czech and former world number one Karolina Pliskova retired with a leg injury in the first set.
Last year's finalist, Jelena Ostapenko, also progressed, while Elisabetta Cocciaretto backed up her win over Coco Gauff to book her place in a maiden WTA 1000 quarter-final.