The Dane, a U.S. Open finalist in 2009 and 2014 but unseeded this year after being sidelined for two months by an ankle injury, dominated from the start and wrapped up victory in just under an hour and a half.
Niculescu, ranked 16 places above Wozniacki in the rankings at 58th, made life tough early on, particularly with her sliced forehand which is a rarity on the WTA Tour.
"I think it's fun (to play her) but also a little frustrating because she makes you feel like you can't play tennis," Wozniacki said.
"You have to be ready to grind and it's not pretty but I got a good workout in there. She made me run a lot."
Wozniacki will face either eighth-seeded American Madison Keys or Japan's Naomi Osaka in the last 16 and said she needed to continue to play aggressive tennis.
"I just need to step in, hit the ball and just go for it," she smiled. "Otherwise I have no chance."
(Editing by Mark Lamport-Stokes)
