PARIS (AP) — Jack Sock cruised into the fourth round of the French Open on Saturday, but he’ll need to get past a much tougher challenge to reach his first singles quarterfinal at a Grand Slam.

The Lincoln native, the last American man in the tournament, reached the fourth round after beating 18-year-old Borna Coric of Croatia 6-2, 6-1, 6-4.

After ending Saturday’s match with a cross-court backhand that Coric netted, Sock soaked up the applause, but the celebration was rather muted. This was the most important singles win at a major for the 22-year-old, who was born in Nebraska, grew up in Kansas City and now is based in Florida.

Sock delivered 31 winners and saved the only break point he faced, winning 30 of 34 first-serve points on Court 2.

Next up for Sock: nine-time French Open champion Rafael Nadal, who has lost just once in his career at Roland Garros. The sixth-seeded Nadal made the fourth round with a 6-1, 6-3, 6-2 win over Andrey Kuznetsov.

Sock, 22, has never played Nadal. The Spaniard’s lone loss in the French Open came in the fourth round in 2009.

Sock upset No. 10 Grigor Dimitrov in three sets 7-6, 6-2, 6-3 in his singles opener and knocked off Spaniard Pablo Carreno Busta 6-7, 7-6, 6-1, 7-6 in the second round.

In doubles, Sock and partner Vasek Pospisil of Canada are due to play Pierre-Hugues Herbert and Nicolas Mahut of France in the third round Sunday.

In women’s singles, only two Americans remain, and they’ll meet in the fourth round after wins Saturday. Top-ranked Serena Williams rallied for a 3-6, 6-4, 6-2 win against Victoria Azarenka, while Sloane Stephens cruised against Tsvetana Pironkova 6-4, 6-1.

After dropping the first set, Williams won the final six games and 10 of the final 12 against Azarenka.

“I was just really down and out in that match, and I just feel like, you know, I just really zeroed in,” Williams said. “I really focused and I really wanted to win that.”

Williams is 28-1 in 2015, 9-0 in three-setters. The 33-year-old American improved to 50-11 at Roland Garros, making her the first woman since 1968, when Grand Slam tournaments admitted professionals, to have that many wins at each major.

She’s never been as comfortable or confident on the French Open’s dusty red clay as with grass or hard courts underfoot, exiting in the second round last year and the first in 2012. She’s been past the quarterfinals once in the past 12 years — in 2013, when she won her second French Open title.

Compare that with Williams’ trophies elsewhere: six apiece from the Australian Open and U.S. Open, five from Wimbledon.

The most significant victory of the 22-year-old Stephens’ career came when she reached her only Grand Slam semifinal by beating Williams at the 2013 Australian Open. Later that year, Stephens found herself in a bit of a brouhaha over less-than-flattering comments she made to a reporter about Williams.

Other fourth-round matchups: Petra Kvitova vs. Timea Bacsinszky, Sara Errani vs. Julia Goerges, and 93rd-ranked Alison Van Uytvanck vs. 100th-ranked Andreea Mitu.

Other men’s fourth-round pairings: No. 1 Novak Djokovic against Richard Gasquet, Andy Murray against Jeremy Chardy, and U.S. Open champion Marin Cilic against David Ferrer.

Djokovic and Murray advanced with straight-set victories over a pair of young Australians seen by many as part of the next wave of tennis stars. Their day might come, but not Saturday.

Murray won his 13th consecutive match by eliminating brash 20-year-old Nick Kyrgios 6-4, 6-2, 6-3, while Djokovic stretched his winning streak to 25 matches on all surfaces by defeating 19-year-old Thanasi Kokkinakis 6-4, 6-4, 6-4.

After wasting a pair of break chances, Kyrgios muttered: “What are you doing out here? Go gardening or something!”

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