Clijsters spent two years away from competitive tennis
Kim Clijsters' comeback gathered pace when the former world number one beat Patty Schnyder 6-2 7-5 to reach the third round of the Cincinnati Open.
The 26-year-old Belgian, playing in her first event after a two-year break during which she gave birth, beat the world number 20 in 70 minutes.
"The first-serve percentage was a lot better than the first match," she said.
"I started making a few little mistakes here and there, but I stayed aggressive and stuck to my game plan."
Unseeded Clijsters dropped just three points as she raced to a 3-0 lead and though Schnyder steadied herself, the first set was a one-sided affair.
Schnyder raised her game in the second but the Belgian broke in the 12th game to set up a clash with Russian sixth seed Svetlana Kuznetsova, the French Open champion.
"I think any match now is a good test," Clijsters said. "Svetlana can play really aggressive tennis and mix it up well. I will have to be on top of my game if I want to give myself a shot at winning."
Second seed Serena Williams made short work of her second-round opponent Kateryna Bondarenko to progress 6-3 6-2.
The nine-time Grand Slam winner powered down 22 aces as she prevailed in little more than an hour against her Ukrainian opponent, ranked 67th in the world.
Williams will now take on Austrian Sybille Bammer, who caused a stir with a 6-0 7-5 success against 13th seed Agnieszka Radwanska.
There were straightforward wins for fourth seed Elena Dementieva - 6-3 6-4 against Belgian qualifier Yanina Wickmayer - and fifth seed Jelena Jankovic, who beat wildcard Maria Kirilenko 7-6 (8/6) 6-3.
Seventh seed Vera Zvonareva and eighth seed Caroline Wozniacki also progressed, but former world number one Ana Ivanovic, seeded 11, came a cropper against Hungary's Melinda Czink 7-6 (8/6) 7-5.