Former champ Jessica Pegula cruises into quarterfinals in Washington, D.C.

WATCH: Top seed Jessica Pegula was victorious in an all-American second round against Peyton Stearns.

WASHINGTON (AP) — Jessica Pegula has a couple of goals this week at the DC Open: trying to earn a third career singles title and building her game leading up to the final Grand Slam of the year.

She's off to a strong start in each department.

The fourth-ranked women's player in the world and tournament's top seed shook off a slow start, beating fellow American Peyton Stearns 6-3, 6-4 Thursday to advance to the quarterfinals of the hard-court tuneup for the US Open. Pegula wrapped it up just before the rain started, happy to fight through some windy conditions and get past a tough opponent.

Pegula won in Washington in 2019 and would love three more victories and another championship before leaving town.

"I definitely want to win the tournament: That's why I'm here," Pegula said. "But at the same time, first tournament on hard (courts) in a little while, so you definitely, I feel like, want to get your movement down, your footing down. ... Working through and problem-solving those things builds confidence, and ideally that's what I want to keep building all the way up until the Open."

Pegula, 29, has never gotten further than the quarterfinals in a Grand Slam. She's coming off a quarterfinal loss at Wimbledon and an exit in the round of 32 at the French Open.

Each of her two singles titles have come on hard court, and this event is an opportunity for the Buffalo, New York, native to fine-tune some things about her play with an eye toward a long run Flushing Meadows.

"I'm not trying to drastically change anything," Pegula said. "But I think just trying little things here and there, and that's kind of how you build confidence little by little. It's just trying different things and not being afraid to try them."

Because she got a bye, the match against Stearns was Pegula's first of the tournament. She likes the rhythm of playing every day and will be right back on the court Friday against Ukraine's Elina Svitolina, who's on a roll after reaching the Wimbledon semifinals and knocking off Victoria Azarenka and Daria Kasatkina in this week.

"She's been competing really, really well and playing very fearless," Pegula said. "It's going to be a tough match. She's been playing at a high level."

The big upset of the day came just before Pegula and Stearns stepped onto stadium court. Sixth-ranked Caroline Garcia, the tournament's second seed, got knocked out in the round of 16 by Marta Kostyuk 6-2, 6-3.

Fans waved Ukraine's blue and yellow flag in the stands after Kostyuk broke Garcia to win the match. She joined Svitolina as women's players from the war-torn country to reach the quarterfinals in Washington, with Kostyuk set to play Liudmila Samsonova from Russia on Friday for a spot in the semis.

On the men's side of the draw, fifth-seeded Grigor Dimitrov advanced to the quarterfinals by beating Emil Ruusuvuori 6-4, 6-3, and J.J. Wolf beat Michael Mmoh 6-4, 7-6(5).

No. 1 seed Taylor Fritz is set to face three-time Grand Slam champion Andy Murray in prime time, though rain delayed the start of the night session opening with Washington-area Frances Tiafoe against Shang Juncheng.