Radwanska, who was down a double break in the first set, struggled with her first serves. But as the match progressed, the Pole's superb shot-making gave Niculescu little chance of recovering.
"I think she has the best hands on tour, very tricky player and very uncomfortable to play against," Radwanska said of her Romanian opponent.
"I knew it was going to be tough and a long one. What can I say? She really made me play my best tennis, so I'm very happy to win that match in two sets."
Kvitova, a two-time Wimbledon champion, came from 3-1 down to win the first set, but Ostapenko continued to play with confidence. She hit 28 winners before wrapping up the match in one hour and 56 minutes.
Ostapenko will next face China's Zheng Saisai, who continued her excellent form at the tournament by beating Canada's Eugenie Bouchard 7-6 (1), 6-1.
Zheng had beaten top-seeded Angelique Kerber on Tuesday.