On a sunny afternoon in Paris, Gauff struggled to handle the Russian Andreeva's power before finding her stride to set up a meeting with Slovakia's Anna Karolina Schmiedlova, who beat American qualifier Kayla Day 6-1, 6-3. A potential quarterfinal clash against Iga Swiatek potentially looms after that.
"Mirra, she's super young and has a big future for her. I remember when I was here as a 15-year-old, she has a lot to look forward to," the 19-year-old Gauff said.
"In the first set, I had chances, we traded breaks and overall I knew the game plan, so I tried to execute it in the second and third sets. We practiced together earlier [before the draw], so I'm sure she picked up things from my game and I picked things from hers."
Andreeva, the 16-year-old who burst onto the scene with two victories over top-20 players at the Madrid Open, forced Gauff onto the back foot with her explosive power from the baseline and took a 4-2 lead, only to allow the American to claw her way back.
In a first set in which both players struggled to hold serve, Gauff went up 5-4 and 30-0 but got broken again before a poor shot at the net in the tiebreak gifted Andreeva the chance to take the advantage in the match.
Andreeva wasted her first two set points and received a warning after hitting the ball into the packed Suzanne Lenglen stands.
She picked herself up, however, to bag the set with a swinging volley.
Andreeva then smashed her racket onto the ground in frustration as Gauff took the upper hand in the second set, winning five games in a row to level the match.
Gauff broke for 3-1 in the decider and did not look back, ending Andreeva's misery on her first match point.
Also Saturday, top-seeded Swiatek of Poland blanked Xinyu Wang of China 6-0, 6-0 with a flawless display to stay firmly on course to successfully defend her French Open title and issue a warning to her rivals.
Swiatek, aiming to win her third trophy in Paris in five years, showed no weaknesses as she cruised into the fourth round.
She has now dropped just eight games in her three 2023 matches in Paris and has won four of the six sets she has played to love.
"For sure, I am happy. It was a very strong performance from me, and I was happy I was disciplined and took care of everything," Swiatek said.
"Every point is important for me, and at the highest level every point matters," the 22-year-old world No. 1 added. "You always have to be kind of disciplined.
"I am going to use that skill later when I have tight matches."
She wasted little time to show who was in charge, breaking Wang three times to seal the first set in 28 minutes.
Wang's strong forehand was supposed to be a major factor, but instead it let her down as she piled up a dozen unforced errors en route to the first of two bagels.
Swiatek, who had also managed the double-bagel feat in Rome last month, refused to be drawn into Wang's power rallies and instead made her opponent run.
She ended her master class after 51 minutes with a lucky net cord on her first match point.
No. 14 Beatriz Haddad Maia dropped the opening set to No. 23 Ekaterina Alexandrova on Saturday before rallying for a three-set victory. She'll face Sara Sorribes Tormo in the fourth round after Tormo advanced in a walkover after Wimbledon champion Elena Rybakina withdrew because of an illness