PARIS — Reigning US Open champion Sloane Stephens needed less than an hour to move into the second round at Roland Garros.

The 10th-seeded Stephens advanced with a 6-2, 6-0 victory over Arantxa Rus of the Netherlands on Sunday at the French Open.

It was Stephens’ first win at a Grand Slam Tournament since claiming her first major title in New York last September.

The American lost in the first round at the Australian Open in January. Rus was in the first round in Paris as a “lucky loser.”

Fourth-seeded Elina Svitolina was a point away from dropping her first set at the French Open before taking eight consecutive games and coming back to beat 68th-ranked Ajla Tomljanovic 7-5, 6-3.

Svitolina is coming off a clay-court title in Rome and is one of a half-dozen players who can move up to No. 1 in the rankings by the end of the tournament at Roland Garros.

But she started about as poorly as possible on Day 1 at the year’s second major tournament: Tomljanovic held at love for a 5-1 lead at the outset. Tomljanovic then served for the set at 5-2 and held a set point but double-faulted it away and got broken there, then again while serving for the set at 5-4.

That was all part of the eight-game run for Svitolina that gave her that set and a 2-0 lead in the second.

Svitolina has reached the quarterfinals in Paris in two of the past three years. She’s never been past that round at any Grand Slam tournament.

France’s Alize Cornet is through to the second round, beating 2012 runner-up Sara Errani of Italy 2-6, 6-2, 6-3.

Cornet, seeded 32nd, is playing her 14th Roland Garros after she was cleared of a doping charge by an independent tribunal earlier this month.