Top seed Anna Chakvetadze has eliminated Australian Casey Dellacqua in the second round of the Pilot Pen Tennis in New Haven.
Dellacqua was beaten 6-4 6-4 and will now turn her attention towards the year's final Grand Slam, the US Open, starting next week in New York.
There were also wins for former world No.1 Amelie Mauresmo, who defeated fifth seed Patty Schnyder in a third set tie-breaker, second seed Daniela Hantuchova, and rising French star Alize Cornet.
Sixth seed Flavia Pennetta bowed out but Danish star Caroline Wozniacki advanced.
In the men's draw, top seed Fernando Verdasco charged into the quarter-finals with a 6-3 6-1 trouncing of Czech Ivo Minar.
Fellow seeds Igor Andreev, Marin Cilic, Andreas Seppi and Mardy Fish, also won through to the final eight.
But second seed Ivo Karlovic was the victim of a huge upset, losing to world No.434 Luca Gregorc of Slovenia 7-6 (7-4) 4-6 6-2.
Meanwhile, Pauline Parmentier and New Zealander Marina Erakovic, the top two seeds, both made first-round exits at the Forest Hill Tennis Classic in New York.
Results from the Pilot Pen Tennis, New Haven
Men's third round
1-Fernando Verdasco (Spain) def. Ivo Minar (Czech Republic) 6-3 6-1
Luca Gregorc (Slovenia) def. 2-Ivo Karlovic (Croatia) 7-6 (7-4) 4-6 6-2
4-Igor Andreev (Russia) def. 16-Victor Hanescu (Romania) 6-4 7-5
6-Marin Cilic (Croatia) def. 11-Jurgen Melzer (Austria) 5-7 6-4 7-5
7-Andreas Seppi (Italy) def. Fabio Fognini (Italy) 6-4 6-2
8-Mardy Fish (USA) def. 9-Marc Gicquel (France) 6-4 6-3
Jesse Levine (USA) def. Steve Darcis (Belgium) 2-0 retired (back)
Mihail Zverev (Germany) def. Robbie Ginepri (USA) 1-6 6-3 6-1
Women's second round
1-Anna Chakvetadze (Russia) def. Casey Dellacqua (Australia) 6-4 6-4
2-Daniela Hantuchova (Slovakia) def. Olga Govortsova 3-6 6-2 7-6 (7-4)
Amélie Mauresmo (France) def. 5-Patty Schnyder (Switzerland) 6-4 3-6 7-6 (9-6)
Sorana Cirstea (Romania) def. 6-Flavia Pennetta (Italy) 3-6 6-4 6-3
7-Alize Cornet (France) def. Katarina Srebotnik (Slovenia) 7-6 (7-3) 4-6 6-2
Caroline Wozniacki (Denmark) def. Monica Niculescu (Romania) 6-3 6-3
First round results from the Forest Hill Tennis Classic, New York
Peng Shuai (China) def. 1-Pauline Parmentier (France) 6-3 6-2
Jamea Jackson (USA) def. 2-Marina Erakovic (New Zeleand) 7-6 (7-4) 7-5
4-Carla Suarez Navarro (Spain) def. Timea Bacsinszky (Switzerland) 6-4 7-6 (7-5)