Stan Wawrinka continued his French Open defence with a comfortable 6-4 6-3 7-5 win over France's Jeremy Chardy.
The Swiss third seed hit 36 winners and will face Serbia's Viktor Troicki in the fourth round.
Richard Gasquet is the first Frenchman into the last 16, beating Australian Nick Kyrgios 6-2 7-6 (9-7) 6-2 to set up a meeting with Kei Nishikori.
In the women's draw, 10th seed Petra Kvitova lost 6-0 6-7 (3-7) 6-0 to world number 108 Shelby Rogers.
Sixth seed Simona Halep was taken to three sets by 18-year-old Naomi Osaka, but Garbine Muguruza made more straightforward progress.
The Spaniard, who has hired coach Sam Sumyk since her run to the Wimbledon final last year, dispatched Belgium's Yanina Wickmayer 6-3 6-0 in 63 minutes.
Andy Murray eased into the last 16 of the French Open with a straight-set victory over big-serving Ivo Karlovic.
The British number one, who has reached the semi-finals in each of the past two years, was dominant in recording a 6-1 6-4 7-6 (7-3) win.
He broke Karlovic's opening serve in each of the first two sets before sealing victory in a tie-break.
The Scot will play another big server in the next round after American John Isner beat Russian Teymuraz Gabashvili.
"It was very close, especially in the third set," Murray said. "He fought right to the end.
"I started quickly and obviously it is great to get off court in a relatively quick match."
British number two Aljaz Bedene will attempt to follow his compatriot into the fourth round when he takes on world number one and top seed Novak Djokovic on Saturday.
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