GUADALAJARA, Mexico -- World No.6 Maria Sakkari, No.10 Caroline Garcia, and No.11 Daria Kasatkina moved one step closer to qualifying for the WTA Finals in Fort Worth, Texas, after tallying opening-round victories at the Guadalajara Open Akron. 

Coming into the final Hologic WTA Tour tournament of the regular season, Sakkari sat at No.10 on the Race to the WTA Finals, one spot out of qualifying behind Veronika Kudermetova, who currently sits in the last qualifying spot. Seeded No.4, Sakkari responded by defeating Marta Kostyuk 6-4, 6-4 to temporarily overtake Kudermetova in the live Race Leaderboard.

Kudermetova plays her first match in Guadalajara on Wednesday against San Diego finalist Donna Vekic. 

In a gritty match that saw Sakkari and Kostyuk combine for 22 break point opportunities, it was Sakkari's play on those big points that proved the difference. Kostyuk generated 13 break points but could only break twice, while Sakkari broke four times from nine chances. With the boisterous crowd willing her to the finish line, Sakkari rallied from 0-40 down in her final service game to close out the win.

"I come from a country that is very far, and I was actually surprised the last year that I got this love from every single Mexican in this tournament," Sakkari said. "I'm very grateful and thankful for that. I'll try and enjoy as much as I can this week because I want to stay until the end. I really like this place."

Sakkari will face either Danielle Collins or Magdalena French in the Round of 16. But before that, the Greek star will be keeping watch on her good friend Vekic's match against Kudermetova. Asked about her upcoming duel against Kudermetova, Vekic admitted she was well aware of the Race implications.

"She's playing really well," Vekic said after her opening win over Laura Pigossi. "I know she's fighting for the Finals. 

"I'm going to try to stop her for my sake and for the sake of my friends that are just behind her also, who for sure want me to win."

While Sakkari is fighting to advance her Race position, Kasatkina is in the position of holding off any challengers in her rearview mirror. Sitting at No.7 in the Race, Kasatkina maintained her position by easing past Zhu Lin, 6-1, 6-2 to advance to the Round of 16.

Watch This: Kasatkina amazing pick-up vs. Zhu Lin

"As much as I was trying to push away the thought of the Finals, to trick myself, I cannot," Kasatkina told WTA Insider. "I just have to accept this pressure and face it the way I can. It's the first time I actually have a chance to compete, not as an alternate, so it's stressful. But the way I am doing on the court, I'm pretty happy.

"I'm not in a bad position. And after this match I'm in an even better position. That's why this was a really important one and now I feel I put the heavy backpack down."

Kasatkina will next face either Monastir champion Elise Mertens or Anna Kalinskaya. 

"This pressure is good," Kasatkina said. "If at the end of 2019 someone tells me in three years you're going to have the pressure to go to the WTA Finals to play, I would say are you kidding me? I cannot believe it. So far it's a very good problem to have."

Sitting at No.6 on the Race to the WTA Finals Leaderboard, Garcia closed out the night session, defeating Canadian qualifier Rebecca Marino, 6-7(2), 6-3, 7-6(5). Marino fired 24 aces in the match but managed just one break of serve on the Frenchwoman, who answered with 13 aces of her own. Garcia led 4-2 in the final set before Marino finally broke through and leveled the set at 4-4.

Highlights: Garcia d. Marino

Marino came within two points of earning her first Top 10 win, but Garcia served herself out of trouble at 5-6, 0-30 to force the final tiebreak. In the tiebreak, Garcia let a 4-1 lead slip before firing an ace at 5-5 to earn match point and converting after 2 hours and 31 minutes. 

Garcia will face either Belinda Bencic or Sloane Stephens in the Round of 16. 

With five qualifying spots for the WTA Finals remaining, 17 players had a chance to qualify for the WTA Finals at the start of the week. After Day 2, that number has been whittled down to 13, with Petra Kvitova, Beatriz Haddad Maia, Ekaterina Alexandrova, and Barbora Krejcikova bowing out.