In 2012, Sharapova completed a career Grand Slam at Roland Garros, adding that trophy to ones from Wimbledon in 2004, the U.S. Open in 2006 and the Australian Open in 2008.
Sharapova has won all eight sets she's played so far this year and will face No. 18 Jelena Jankovic or 54th-ranked Jamie Hampton in the quarterfinals.
The 20-year-old Stephens, who upset Serena Williams en route to reaching the semifinals of the Australian Open in January, fell to 1-8 against women ranked in the top five.
Stephens lost in the French Open's fourth round for the second year in a row. Last time, at 19, she was the first U.S. teenager to make it that far in Paris since Williams did it in 2001.
During an on-court interview after Monday's match, Sharapova, who's 26, was asked about facing a member of her sport's "younger generation."
"I still like to consider myself young," Sharapova said with a smile. "Maybe not the 'young generation,' but somewhere in the middle."
With wind whipping around Court Philippe Chatrier some spectators huddled under blankets Sharapova managed to handle the conditions well.
At 3-all, she held three break points, and she took that game when a good return off a 103 mph serve forced Stephens into an error. That little lead was enough to take the opening set, which Sharapova served out at love.
Stephens earned three break points the entire match and took advantage of only one. They all came in the second set's second game, when a cross-court forehand winner by Stephens made it 1-all.
But Sharapova broke again to go ahead 3-2 when Stephens put a backhand into the net. From there, Stephens' body language was filled with slumping shoulders and a hanging head.