The Spaniard has not won a Grand Slam title since 2014 but served notice of his return to form with a dominant performance on Rod Laver Arena.
Asked if he was now at 100% after his injury struggles last year, Nadal replied: "I am here and I am happy to be here. With no injuries now so I cannot ask for more.
"I suffered injuries in my career but on balance I had a lot of success and amazing memories from all the places I have played so I cannot complain."
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Nadal professed to having some problems adapting to the late start, but felt he improved as the match wore on.
"It was a good match," he added.
I didn’t play before in the night this year so the conditions changed a lot: the ball is much slower and it was tough to adjust at the beginning. When the match was going I was playing better and better. Marcos is a great, great player, especially on this court, and I wish him all the best for the rest of the season
Djokovic loomed as a potential semi-final opponent for Nadal but the Serb's five-set upset by wildcard Denis Istomin shook up the draw and left the Spaniard as the sole Grand Slam champion in the bottom half.
Nadal has had two lean years at the majors, but on the same Rod Laver Arena where Djokovic fell to Istomin, the 14-times major champion showed enough of the old passion and firepower to suggest he may yet go deep in the second week at Melbourne Park.
"What Novak did here is just amazing," said Nadal, paying tribute to the fallen 'Big Four' colleague who edged him in an epic for the 2012 title, the longest Grand Slam final played. "Six victories here, six titles. For a lot of years he has been in the semi-finals, finals, and winning here. So it's normal then (to lose). It's not possible to be every time in that situation."
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Nadal needed only two hours and 13 minutes to defeat Cypriot Baghdatis, whose run to the 2006 final as an unseeded 20-year-old is part of Australian Open folklore.
The 31-year-old Baghdatis saved two match points but Nadal closed out the one-sided contest with a smoking cross-court forehand, his 32nd winner for the match, and punched the air in triumph as the terraces roared.
Nadal, 30, faces German talent Alexander Zverev next, a player tipped for a big future in the game. Nadal praised the 24th-ranked 19-year-old, who upset three-times grand slam champion Stan Wawrinka last year to win his maiden ATP title in St. Petersburg.
"He is a great player, one of the best players of the world, without a doubt, today," the Spaniard said. "He's a player that is for sure one of the next grand slam winners. He has a big chance to become the future world number one. I need to (have) a very, very high rhythm to try to not let him play in comfortable positions. That's what I am going to try."