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.
Murray appeared to be toying with 27th seed Bautista 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.
Murray was thrilled to have thrashed an opponent who has been in top form of late.
"He's won a lot of matches lately, he won on the grass and he's made a lot improvements," he said.
"There were a lot of close games and it's good to get it done in straight sets. He's the best opponent I've played so far and as a step up I felt I responded well.
"There's a few things I could improve on but it's a good first week. I had enough long matches in the French Open to get me physically ready."
The home fans were out in force on Centre Court, and Murray paid tribute to the support he has received this week despite the pressure the extra attention brings.
"Once I get out on the court I really enjoy it. I try to avoid it away from the court but on the court it's great, the atmosphere has been great, it gives me a big lift and I am going to need it as the tournament goes on. "
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.
The Scot's path looks set to become more complicated in the next round against towering South African 20th seed Kevin Anderson - and Murray was wary.
"Like Roberto, he's playing the best tennis of his career, he's made some improvements this year. He's a big guy with a big game so I need to be sharp and return well if I want to win."
- Sports & Recreation