The 11-time champion showed no sign of the knee problems which forced him to quit ahead of an Indian Wells semi-final against Roger Federer a month ago.
The 32-year-old had expressed pre-tournament caution regarding the health of his knee -- a worry which appeared to be groundless after a 76-minute masterclass.
"I'm happy for this very positive start. I had good feelings on court," he said.
Nadal collected the opening five games of the afternoon in 17 minutes as he set the tone for another dominant display in the principality.
He was equally in control during the second set, where he saved three break points in the fourth game and two more in the sixth.
"It was a great start, it's good to be back here," the 17-time Grand Slam winner said, keeping talk of his knee to a minimum.
"I can't pretend to not have pain at all, but professionals normally play with pain," Nadal said.
"It's part of the sport at the highest level and it's no limitations at all. I was able to move well and be confident with the things that I did."
Bautista Agut has now lost to his Spanish countryman in all three of their meetings, while Nadal improved his incredible record here to 69-4 as he takes aim at a fourth consecutive title at the event.
"This is just the first match and it's been a very positive start," Nadal said. "The results say that."
Roland Garros finalist Dominic Thiem, who lost to Nadal in Paris last June, beat Slovakia's Martin Klizan 6-1, 6-4.
Thiem, who won the Indian Wells title over Federer, made a successful switch to his favourite surface as he prepares for the pre-French Open sequence of events.
Fourth seed Thiem won with a break in the final game after Klizan held a 40-0 lead.
- Upbeat Zverev -
Alexander Zverev rediscovered traces of his best form with a 6-1, 6-4 defeat of Canadian teenager Felix Auger-Aliassime.
The German, locally based, reached the third round as he tamed the 18-year-old who broke through for a Miami semi-final last month.
The 21-year-old Zverev played the semi-finals in Monte Carlo a year ago but has yet to hit his stride this season.
That may be starting to change.
"This is the first time this season I've felt really healthy," said Zverev, who lost prematurely at both Indian Wells and Miami, as well as in Marrakech last week.
"I've been training well but haven't been able to take that into matches.
"I live just 500 metres from here, I'm comfortable on this court. I'm starting to feel better about my game.
"I'm really ready for the clay season."
Zverev swept the opening set in 30 minutes but had to get through a series of three straight breaks of serve between him and his opponent before finally advancing in 78 minutes.
The third seed will next face Italy's Fabio Fognini, who reached the third round when French opponent Gilles Simon withdrew because of back problems.
Greek sixth seed Stefanos Tsitsipas moved ahead, defeating Mikhail Kukushkin 6-3, 7-5.
"I need to maintain my focus, my concentration, my aggressive mindset when I'm on the court," Tsitsipas said.
"If all these are combined, then I have nothing to fear and I have nothing to be afraid of when I'm on the court.
"This is the first big clay court tournament, not everyone is very well prepared for that. It's been a long hardcourt court season before the clay."
Britain's Cameron Norrie defeated Marton Fucsovics of Hungary 7-6 (7/3), 6-3, while Pierre-Hugues Herbert stunned 2018 finalist and fifth seed Kei Nishikori 7-5, 6-4.