The heat at the U.S. Tennis Center caused No. 10 seed Victoria Azarenka to collapse and she eventually had to be taken off the court in a wheelchair.
Gisela Dulko won the match by forfeit and Azarenka was eventually diagnosed as having a slight concussion.
Clijsters, the No. 2 seed, spent only 56 minutes on the court while defeating Sally Peers 6-2, 6-1.
The third-seeded Williams, who has been out of action since Wimbledon due to a knee injury, eliminated Rebecca Marino 7-6 (7-3), 6-3. In the third round, Williams will meet Mandy Minella, who prevented an anticipated rematch between Williams and Tsvetana Pironkova.
Pironkova, who shocked Williams in this year's Wimbledon quarterfinals, lost to Minella 6-4, 6-0.
Azarenka said she fell and bumped her head while running sprints in a nearby gymnasium prior to her match and after being checked out by the medical staff was cleared to play. She was overcome by the heat while trailing 5-1 in the first set.
In other second-round action Wednesday, Samantha Stosur was a 6-1, 6-4 winner over Anastasia Rodionova and sixth-seeded Francesca Schiavone, this year's French Open champ, breezed by Maria Elena Camerin 6-2, 6-1.
Elena Dementieva reached the third round with a 6-3, 6-4 decision over Sybille Bammer and Shahar Peer defeated Pauline Parmentier 6-2, 6-3. No. 13 seed Marion Bartoli was surprised by Virginie Razzano 7-5, 6-4.
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