No.6 seed Coco Gauff of the United States, No.9 seed Maria Sakkari of Greece and No.5 seed Caroline Garcia of France kicked off their 2023 Mutua Madrid Open campaigns with straight-sets second-round wins on Thursday, after first-round byes.

Gauff and Sakkari are potentially on track for a Top 10 showdown in the Round of 16 if they can each win their next match.

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Gauff came back from an early break down in the first set to oust Spanish qualifier Irene Burillo Escorihuela 6-4, 6-1 on Manolo Santana Stadium. Gauff took 1 hour and 17 minutes to topple the World No.316 and reach the Madrid third round.

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Local favorite Burillo Escorihuela, who beat Kaia Kanepi in the first round for her first career win over a Top 100 player, outlasted Gauff in rallies early en route to a 4-2 lead. Gauff got back on serve at 4-4, but fell behind 0-30 for the second straight service game.

However, Gauff found exceptional serves in each of those service games to pull her way out of danger, then broke Burillo Escorihuela for the second time in a row to capture the first set.

Gauff built a 5-0 lead in the second set after notching her ninth straight game, then served out the match at 5-1 to advance. Gauff finished the match with 16 winners, including four aces, to Burillo Escorihuela's 13 winners.

Gauff will face another Spaniard in the third round -- No.26 seed Paula Badosa. Spanish No.1 Badosa defeated Italy's Elisabetta Cocciaretto 6-3, 4-6, 6-4 on Thursday.

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Sakkari also won her first match of the week on Thursday, defeating Dutch qualifier Arantxa Rus 6-4, 6-4 in 1 hour and 35 minutes.

Sakkari improved to 5-0 against Rus (10-1 in sets) with her latest victory over the World No.107. Sakkari slammed six aces and saved six of the seven break points she faced in the clash.

Highlights: Sakkari def. Rus

The Greek had to fend off three break points in the lengthy final game of the match, but Sakkari converted her second match point to book her spot in the Madrid third round.

Sakkari will now face Spanish wildcard Rebeka Masarova in the third round, after 74th-ranked Masarova upset No.20 seed Donna Vekic 6-1, 7-6(5). Another win would put Sakkari into the Madrid Round of 16 for the second straight year.

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Garcia followed with a 6-3, 6-4 victory over Yulia Putintseva of Kazakhstan. Putintseva had won all three of their previous matches, but Garcia finally got on the board in their head-to-head with a 1-hour and 35-minute win.

French No.1 Garcia, who reached the Madrid semifinals in 2018, fired 45 winners in the match, including 18 aces. Garcia's aggressive play on both serve and return gave her a commanding 6-3, 4-0 lead and she was a point away from reaching 5-0 in the second set.

Highlights: Garcia's top winners

However, World No.51 Putintseva pulled herself back into the match, reeling off three games in a row and holding two break points to level the second set at 4-4. Garcia, though, regrouped to keep her break advantage at 5-3, and she served out the match at love two games later.

Garcia will face Mayar Sherif of Egypt in the third round, after Sherif upset No.30 seed Anhelina Kalinina 6-2, 7-6(3). Garcia won their lone previous match earlier this year, on the hard courts of Monterrey by 6-0, 6-4.