The Brit required just an hour and 35 minutes to ensure a place in the last 16 with a 6-2 6-3 6-2 win on Centre Court.
After easing to straightforward victories over David Goffin and Blaz Rola in the opening two rounds, Murray was in no mood to relent against the world number 23.
He was rarely tested by the Spaniard, who only reached the fourth round of a grand slam for the first time at the Australian Open in January.
It was a typically energetic display of impressive defence, power and accuracy from Murray, the home favourite racking up 43 winners on his way to victory.
Moments of consolation were rare for Bautista Agut, although he was able to snatch a service game from Murray in both the second and third sets after going a double break down on each occasion.
However, despite the sporadic spells of defiance from the 26-year-old, it proved short work for Murray as the third seed set up a fourth-round clash with Kevin Anderson of South Africa.
"There were a lot of close games and it's good to get it done in straight sets," Murray told BBC Sport.
"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."