Radwanska, No. 4 in the world rankings, stopped Alexandra Cadantu 6-4, 6-0. Two of the games she lost in the first set were on breaks but she lost only six points on serve -- and an even more impressive three points when receiving -- in taking all the games in the second set.
Kirilenko posted a 6-3, 6-3 decision over qualifier Chan Chin-Wei. Kirilenko had six double faults and was good on less than half of her first serves. She countered that by winning 52 percent of the points off Chan's serve and finishing off five of her six break chances.
Jang Su-jeong, invited into the draw as a wild card, ousted fourth-seeded Klara Zakopalova 6-3, 6-1 in just 64 minutes. She had six breaks while winning nearly two-thirds of the points when Zakopalova served.
Eighth-seeded Annika Beck topped Risa Ozaki 3-6, 6-6 (7-5), 6-4 and qualifier Ons Jabeur defeated Nastassja Burnett 7-5, 6-0.
Also Tuesday, as the first round was completed, Estrella Cabeza Candela beat Mandy Minella 7-5, 6-4; Irina-Camelia Begu won 6-3, 6-4 over Han Xinyun and Kimiko Date-Krumm got past Heather Watson 3-6, 6-3, 6-4.
Notable deaths of 2014 [PHOTOS]
Julius Randle breaks leg during NBA debut