No. 1 seed Cibulkova saw off wildcard Fanny Stollar 6-3, 6-3 Wednesday while second seed Zhang advanced to the last 16 in Budapest with a 6-3, 6-2 win against Arina Rodionova.
Defending champion Timea Babos made light work of her first round opponent Tatjana Maria.
Babos, who claimed a career-third WTA title at the Taiwan Open recently following doubles success at the Australian Open, cruised into round two with a 6-1, 6-0 victory and dropped just three points against Germany’s Maria. Babos will take on Germany’s Mona Barthel next.