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.
The 17-times Grand Slam winner was never seriously challenged again, and moved seamlessly into the third round where he will play either Alex de Minaur or Henri Laaksonen. (Reporting by Jonathan Barrett in MELBOURNE Editing by Christian Radnedge)