The home favourite, attempting to defend the title he won last year to become the first Briton to win the men's singles for 77 years, turned the late evening Centre Court duel into a one-sided romp.
Spinal surgery and his inability to reach a final since that surreal day last July meant there had been question marks over his ability to win back-to-back titles at the All England Club.
The third seed proved that he was up to the task of carrying the nation's hopes once more.
"I'd say I'm happy with where my body's at right now. Physically I feel good. My back feels much better than it did at this stage last year, so that's a big positive for me," said Murray, who had back surgery last September.
"I've spoken to a few people that have had surgeries... they said (it took) six to nine months from when they started playing again until they actually started to feel their best.
"I'm fairly happy with where I'm at just now."
Murray appeared to be toying with 27th seed Bautista Agut for most of the match and could even afford a third-set lapse when he dropped serve at 4-0.
The third seed has won his past 16 matches at the All England Club, beginning with his gold-medal run at the 2012 Olympics, and so far at this year's championships he has conceded a mere 19 games in three matches.
"You can lose a slam in the first week by playing three five-set matches or two five-set matches. They do take their toll a little bit," said Murray.
"If you can get through the matches quickly.... I haven't used up too much energy, which is good. It's been a good first week."
After such a spectacular run to the second week, Murray's only gripe was that his mother was not around to offer her support, opting instead to watch his brother Jamie's doubles win.
"It's a shame we were on at the same time because none of my family came to watch me. I am obviously number two son," the Scot joked.
His path might become more complicated in the next round against towering South African 20th seed Kevin Anderson.
(Reporting by Pritha Sarkar and Martyn Herman, editing by David Goodman/Greg Stutchbury)
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