The second seed overcame an early first set challenge from the Australian, who should have secured a break-of-serve with the scores locked at 3-3.
Ebden missed a backhand volley off an unexceptional passing shot - and it proved costly.
The Australian was broken the next game, succumbing with a double-fault, and the Spaniard went through the broken line of defence, securing the set and an early break in the second.
"I started a little bit slow ... then I saved that game at three-all," Nadal said.
"After that, things changed. I think I played well."
Sensing an early end to the proceedings, the crowd tried to lift one of its few remaining local hopes, while at the same time being dazzled by the Spaniard's control of the court.
The 17-times Grand Slam winner was never seriously challenged again, and the third set became an exhibition match.
At one stage, Ebden simply shrugged after Nadal unleashed a wild forehand winner that was yet completely under control.
Nadal, who showed no signs of discomfort from a thigh strain that troubled him ahead of the first major of the year, will play Alex de Minaur in the third round, marking his third consecutive match against an Australian. (Reporting by Jonathan Barrett in MELBOURNE Editing by Christian Radnedge and Alexander Smith)