Coco Gauff's won her first match as the World No.2 on Thursday in Berlin, as the top seed at the ecotrans Ladies Open saved three set points in a tense first set before ousting Ekaterina Alexandrova, 7-6(6), 6-2. 

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Gauff, a 2022 semifinalist in Berlin, is through to the quarterfinals at this grass-court tournament for the second time. She lost to eventual champion Ons Jabeur in the semiinals two years ago. The eighth-seeded Tunisian will be Gauff's next opponent. 

From a tight first set to an easy finish, here are our top takeaways from Gauff's first match of the grass-court season, which lasted 1 hour and 20 minutes in total. 

Twelve months later, Gauff flipped the script: Gauff and Alexandrova were playing in Berlin for the second year in a row; last year, also in the Round of 16, Alexandrova tallied an emphatic 6-4, 6-0 win over the then-No.5 seed on her way to the semifinals -- a match Gauff said afterward she didn't even remember playing.

"I'm a different player from last year. She's a great player to play, especially on grass ... so I knew it was going to be tough," Gauff said in her on-court interview. 

Alexandrova came from 4-2 down in the first set to force a tiebreak, as her first-strike tennis found its mark more often than not over the match's first hour. Gauff's only double fault of the first set put Alexandrova up 6-3 in the tiebreak, but she didn't win another point. A double fault of her own, a backhand wide, and a missed backhand return erased all three chances Alexandrova had to win the set -- and another double fault later sealed the set for Gauff. 

"When you're down in those points in tiebreaks, I just tell myself just to get one, and then one point turns into two," Gauff said. "I was just hoping she wouldn't ace me on one of those points. I was just hoping I could get a ball in the court."

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The stats were serve-forward: As Gauff noted, the two players are often lifted, or impeded by, how successfully they serve. They combined for 11 aces and were only pushed to deuce in one service game -- Alexandrova's second in the first set, where she saved a break point for 2-2.

But after capturing the tight first set, Gauff grew in confidence on both sides of the ball. She lost just four points on serve in the second set, and broke Alexandrova twice -- first at love at 1-1, then at 15 in the seventh game.

Pegula holds off Vekic to reach fifth quarterfinal of year

Pegula joins Gauff in quarterfinals: Gauff was joined by doubles partner and No.4 seed Jessica Pegula, who came through two tight sets to defeat wild card Donna Vekic 6-4, 7-5.

Pegula reprised the result of her only previous meeting with Vekic, in the 2022 Wimbledon first round, to reach her fifth quarterfinal of 2024. The 30-year-old Pegula had lost to No.400-ranked Aleksandra Krunic last week in 's-Hertogenbosch, the first tournament of her return from injury but was sharp at net and clutch in the closing stages of the second set against Vekic.

Pegula will next face qualifier Katerina Siniakova, who notched her 10th career Top 10 win (and second of the season) with a 6-4, 6-4 upset of No.6 seed Zheng Qinwen. Pegula holds a 2-1 record against Siniakova overall, but the Czech won their only previous meeting on grass 6-3, 5-7, 6-4 in the 2021 Bad Homburg second round.