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Second seeded Sharapova triumphed in 1hr 29min and now faces either Serbian 18th seed Jelena Jankovic or US hope Jamie Hampton.
Sharapova, who in beating Sara Errani in last year's final became the sixth player in the Open era to complete a full collection of Grand Slams, overcame early resistance from a rival she had beaten twice in as many previous meetings as a crunching pair of forehands saw her take the opening set in 37min.
The pair traded breaks at the start of the second set before Stephens dug in to hold for a 2-1 lead.
But Sharapova stepped through the gears to see off the Australian Open semi-finalist as Floridian Stephens, 20, gifted her a final break by hitting long on match point.
"I knew this was going to be a really hard match so I'm delighted to be in the quarter-final," said Sharapova, who now has an extra day to relax.
"Am I pleased to have finished my match a day before my next opponent? We don't choose the scheduling, it just depends how it goes. I'm just pleased to be through to the next round."
French Open fourth round results (x denotes seeded player):
Men:
Fourth round:
Novak Djokovic (SRB x1) bt Philipp Kohlschreiber (GER x16) 4-6, 6-3, 6-4, 6-4
Tommy Haas (GER x12) bt Mikhail Youzhny (RUS x29) 6-1, 6-1, 6-3
Rafael Nadal (ESP x3) bt Kei Nishikori (JPN x13) 6-4, 6-1, 6-3
Stanislas Wawrinka (SUI x9) bt Richard Gasquet (FRA x7) 6-7 (5/7), 4-6, 6-4, 7-5, 8-6
Women:
Fourth round:
Maria Kirilenko (RUS x12) bt Bethanie Mattek-Sands (USA) 7-5, 6-4
Victoria Azarenka (BLR x3) bt Francesca Schiavone (ITA) 6-3, 6-0
Maria Sharapova (RUS x2) bt Sloane Stephens (USA x17) 6-4, 6-3
Jelena Jankovic (SRB x18) bt Jamie Hampton (USA) 6-0, 6-2
