Clijsters, playing in just her third tournament of the year and second since a semifinal loss in the Australian Open, raced past Kateryna Bondarenko 6-2, 6-1. She won half the points off Bondarenko's serve, claiming four of the 16 break-point chances she had.
Clijsters also won three-quarters of the points on serve, dropping just four points in four games serving in the second set. Her play this year has been limited by a hip injury.
Urszula Radwanska dispatched fourth-seeded Flavia Pennetta 6-1, 6-1 in a second-rounder. Radwanska won two-thirds of the points in the match, losing eight across seven service games.
Third-seeded Dominika Cibulkova got past Shahar Peer 6-2, 7-6 (7-5) and No. 8-seeded Nadia Petrova beat Anabel Medina Garrigues 7-5, 6-3. Cibulkova and Petrova, who will meet in the quarterfinals, each had five breaks Tuesday.
The first round was completed with Daria Gavrilova taking a 48-minute, 6-1, 6-2 rout of Yanina Wickmayer and Sofia Arvidsson edging seventh-seeded Jelena Jankovic 6-2, 3-6, 6-4.
Jankovic was coming off two three-set matches Sunday and a loss Monday to Melanie Oudin in the finals of the AEGON Classic in Birmingham, England. Wickmayer was the runner-up in Saturday's final at Bad Gastein, Austria.