Martic, the No. 5 seed escaped with a 4-6, 6-4, 7-5 win over Erika Sema in a match that took 2 1/2 hours. Martic finished off both of her break-point chances in the third set, during which she won just four more points than Sema.
Dokic, seeded seventh, was an easy 6-3, 6-1 winner over Kristina Mladenovic. She lost just 11 points over eight service games, saving both break points she faced.
Olga Rogowska defeated Elitsa Kostova 6-4, 6-0 by winning 12-of-15 receiving points in the second set in another first-round match. Also, Misaki Doi won nearly two-thirds of the points over the second and third sets in a 4-6, 6-1, 6-2 victory over Olga Puchkova and Kurumi Nara beat Noppawan Lertcheewakarn 6-4, 6-3.
World No. 5 Agnieszka Radwanska, coming off a win at the Dubai Duty Free Tennis Championships, is the top seed in Malaysia.