The 17-times Grand Slam victor was never seriously challenged again, and the third set became an exhibition match.
That run looked in danger when Laaksonen came from two sets down to force the round-two match into a deciding set.
Meanwhile Nadal said he was well aware of de Minaur's prodigous talent.
While compatriots Nick Kyrgios and Bernard Tomic have attracted negative headlines after round-one Melbourne Park exits, de Minaur has garnered support with his fighting spirit.
"Every time I step out on court, I leave 150 per cent out there".
"You want the players in the locker room to know you as that kid that fights 'til the end, has that never-say-die attitude".
Victory at the Sydney International last week - his first ATP tour victory - has been followed by a strong start at the Australian Open after the Sydneysider dug deep to topple Swiss qualifier Henri Laaksonen in a five-set thriller on Wednesday night.
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"I think he improved a lot during the last three years".
"I think for me I definitely have to go through a minor adjustment maybe from Perth- which was a faster court", continued Federer.
In a column for La Gazzetta dello Sport dello Sport the former world No. 12 singles player and current Sky Sport commentator Paolo Bertolucci previewed the upcoming Australian Open. "I'm never taking that for granted".
Nadal admitted he got off to a "slow start" but he still finished off Ebden in rapid fashion to reach the third round. He is winning a lot of matches.
De Minaur, who spent time growing up in Spain, said he recalled watching Nadal win his sole Australian Open on television in 2009.
"I just feel like its really important to have fast enough courts for night session conditions you know as the main matches are being played there because if you keep it slow-slow I mean at night the ball doesn't move so from that standpoint I think they have done a a nice job of speeding up the courts", said Roger Federer.
"It's going to be incredible, just to step out there on court with him", de Minaur said.