Wozniacki was posed a few problems by the unconventional Romanian but she remained in charge to secure a 6-2 6-2 victory on Hisense Arena.
Niculescu, the 31st seed, entertained the crown with her style - hitting double-handed groundstrokes on both sides as well as mixing it up with the occasional sliced forehand and foray to the net.
Wozniacki, though, rattled through the first set in just over half-hour, while the 21-year-old only blotted her copybook when she was broken serving for the match.
The Dane responded by breaking straight back to secure place in the last 16 without dropping a set so far.
"There's not too much rhythm playing against Monica," Wozniacki said.
"She slices the ball from both sides, she can play high and she can play aggressive.
"You need to be fast on your feet to win the points because she's so fast."
Caroline Wozniacki again attempted to play down the significance of her number one ranking.
And she was eager to focus afterwards on on-court matters rather than dwell too long on how her progress would affect her standing.
"To be honest I just play," she said.
"I want to try to do my best here and whatever happens, happens.
"I have proven myself for the last two years. I have finished number one twice in a row.
"And for me the most important thing is to keep on improving. If I do that I know I can play on a very high level.
"If you win tournaments, then the ranking will be there automatically."
Wozniacki displayed a more attacking game on Friday, matching Niculescu's frequent trips to the net and displaying a nice touch, especially on the backhand side.
She added: "I've worked quite a bit on my volleys.
"I still think I could have finished a few more points up there but I'm improving and I'm trying to move in when I can."
Wozniacki will face Jelena Jankovic in the fourth round after the Serbian saw off Christina McHale.
Jankovic, the No.13 seed, was forced to work hard for the first set but she moved through the gears to claim a 6-2 6-0 victory over the American.