The Russian was at her most clinical to seal a last-eight clash with old sparring partner Jelena Jankovic.
While Sharapova made her breakthrough in stunning fashion by winning Wimbledon as a 17-year-old in 2004, Stephens's ascent has been more gradual and reaching the Australian Open semi-finals this year after beating Serena Williams has been the 20-year-old's standout moment.
"20 is the new 17," Sharapova said.
"I think she has a tremendous amount of potential.
"There's a lot of room for a few things to improve and I think she will. I think she has a big game. She has big strokes, a pretty good serve.
"If she's in the right hands at the right time, I'm sure she's gonna have a great career."
Defending champion Sharapova beat Stephens easily in Rome in the build-up to Roland Garros but Monday's clash was a more competitive affair with nothing to separate the players in the opening six games on Chatrier.
Sharapova then pounced as Stephens faltered on serve for the first time, converting her third break point.
Stephens did break Sharapova's serve in the second set but the Russian world number two responded with two of her own.
The only thing to worry Sharapova was the size of the birthday cake defending men's champion Rafa Nadal was presented with on court after his fourth-round win.
"I saw Nadal finish his match, and that was a pretty cool cake he received," said Sharapova who has started up her own candy company. "I was a little bit jealous.
"He's not 30 yet, he's 27. He gets that great cake."
Jankovic battered unseeded American Jamie Hampton 6-0 6-2 in the last match of the day.