The pair walked onto Court Philippe Chatrier at 1913 CET after a day of rain interruptions, before the top-rated Frenchman, seeded the 13th here, lost the first set 6-3 to the Swiss but pulled back the second 6-4.
He will resume the match against the 17-times major winner in Monday's second match on the central court not before 1230.
The winner will play another Swiss Stan Wawrinka in the quarters after the eighth seed saw off France's Gilles Simon 6-1, 6-4, 6-2 on Court Suzanne Lenglen.
Alize Cornet felt frustrated as her first last 16 appearance of her home Slam was stopped by rain when she went 5-0 down, and a tight call went against her on break point down at 5-5 in the second set.
Her 20-year-old opponent Elina Svitolinaof of Ukraine wrapped it up 6-2, 7-6 (9) to set up a quarter-final against with former champion and world No 1 Ana Ivanovic.
The Serbian seventh-seeded Ivanovic, who'll be appearing in the quarter-finals at Roland Garros for the first time since winning the title in 2008, beat Russian Ekaterina Makarova 7-5, 3-6, 6-1.
Two of the scheduled women's fourth-round matches were postponed, namely Sharapova's clash against Czech 13th seed Lucie Safarova and Italian Flavia Pennetta's meeting with Spain's Garbine Muguruza.
Elsewhere at Roland Garros, China's doubles specialist Zheng Jie suffered a third-round exit as her partner Chan Yung-Jan and Zheng lost to Spaniards Silvia Soler-Esino and Maria-Teresa, 4-6, 6-4, 7-6 (6).
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