Williams withdrew from her semi-final at Indian Wells last week with the injury and said upon arriving in Miami that this tournament would involve "managing pain".
But the 19-times Grand Slam winner was too much for Niculescu, ranked 70th in the world.
Niculescu made ample use of her effective slice and played some clever tennis and forced a series of entertaining rallies but Williams was always in control.
The world number one said her knee injury had barely bothered her at all.
"I really didn't feel it today, to be honest," Serena said."Once you step out on the court you have so much adrenaline going. The adrenaline kind of kills it. So I was surprised. I felt pretty good."
The match was scheduled for Friday but was postponed following a rainstorm in South Florida meaning Williams will be back on court on Sunday against fellow American, qualifier Catherine Bellis.Canadian Bouchard lost 6-0 7-6(4) to Maria.
Bouchard was outplayed in the first set, but provided a strong fightback in the second taking a 5-3 lead.
But Maria, whose last win over a top-10 opponent was five years ago against Li Na, rallied to take the set and match.
"It is the best win I have ever had," said Maria, "I just didn't think she was comfortable against my style."
Maria has returned to tennis after giving birth to a daughter 15 months ago and has worked her way back to the tour via the ITF circuit.
Venus Williams, who has won Miami three times, enjoyed a 6-3 7-6(3) win over Australian Samantha Stosur.Fourth seed Caroline Wozniacki battled past Estonian Kaia Kanepi and into the fourth round, winning a tough match in windy conditions 4-6 6-1 6-3.
Germany's Angelique Kerber beat Britain's Heather Watson 7-5 3-6 6-4 while Italy's Sara Errani defeated Russian Anastasia Pavlyuchenkova 6-1 7-6(5).
(Editing by Gene Cherry/Greg Stutchbury)
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