Now among the leading contenders for a maiden grand slam title with defending champion Coco Gauff and four-time winner Iga Swiatek out, the Russian will next face Marta Kostyuk, who beat fellow Ukrainian Elina Svitolina in three sets.
The 19-year-old Andreeva wasted little time asserting herself in front of a sparse crowd beneath the Court Philippe Chatrier roof on Tuesday, racing through the opening set in 24 minutes.
Cirstea, playing her third grand slam quarter-final in her final year on the circuit, steadied herself early in the second set and recovered a break at 3-3, but the 36-year-old could not halt the Andreeva juggernaut.
Andreeva, who reached the semi-finals two years ago, forced an error from Cirstea's racket to break again and she closed out the victory with a forehand bullet, before walking to the net to give her beaten opponent a warm hug.
Kostyuk came through an emotional all-Ukrainian match to reach a grand slam semi-final for the first time as she beat Svitolina 6-3 2-6 6-2 later on Tuesday.
The 23-year-old Kostyuk dedicated her victory to the Ukrainian people, as tears rolled down her cheeks during the on-court interview.
"I want to start with this historical match I played with Elina. We had a difficult night in Kyiv, so many people dead. So I give this match to the Ukrainian people and their resilience. Slava Ukraini," the 15th seed said.
"I want to point out Elina and her impact on Ukrainian tennis, on me and on everyone watching. She's an unbelievable fighter. I'm so happy to be through, but I want to thank her for this incredible match."
Kostyuk surged into a 4-1 lead under the closed roof of Court Philippe Chatrier before Svitolina clawed a break back in front of a sparse crowd.
But Kostyuk broke again to move 5-3 ahead and sealed the opening set when seventh seed Svitolina sent a forehand long.
The momentum shifted in the second set as Kostyuk's serve deserted her, allowing Svitolina, who has now lost in the quarter-finals at Roland Garros for the sixth time, to level the contest.
The decider turned into a tense scrap, with the first five games going against serve.
Pointing her index finger to her head after finally holding for a 4-2 lead, Kostyuk steadied herself before another break and a comfortable hold secured victory.
