The two former Qatar champions last met at the Australian Open in 2019, when Bautista Agut claimed a marathon five-set victory.
But that was the Spaniard's only victory in four matches against Murray and the former British number one had appeared to be gaining in confidence during his first-round victory over Taro Daniel.
That confidence quickly drained away, however, after Murray lost the first point on a backhand error.
A couple of wild groundstrokes from the three-time Grand Slam winner also set the tone for a one-sided first set as the world number 16 Bautista Agut imposed his will on the contest.
Bautista Agut did not lose a point on Murray's opening service game and broke twice more to complete a first-set whitewash.
Murray finally held serve to make it 1-1 at the start of the second set but the Spaniard remained in control.
Bautista Agut pinned Murray back behind the baseline with the depth of his shots to dominate the extended rallies.
With Murray unable to dent Bautista Agut's serve, the fourth game of the second set was to prove crucial.
Murray found a succession of first serves to lead 40-0, but Bautista Agut took advantage of a couple of loose forehands to level and then fired a volleyed winner after setting up a first break point.
The Scot's frustration grew in the final game as he smacked his racket against the court after Bautista Agut delivered an ace to get back to 30-30 after being 0-30 down.
Another ace set up match point and Murray then missed a forehand wide to confirm one of the heaviest defeats of his career.
Evans also out
Fifth seed Dan Evans also went out at the round-of-16 stage as Alejandro Davidovich Fokina claimed a 4-6 7-5 6-4 victory.
The British number one had beaten world number 47 Davidovich Fokina - 19 places below Evans in the rankings - in their only previous ATP tour meeting in Stockholm last year.
After two closely-fought sets, the Spaniard's first three service games in the final set all went to deuce but Evans was unable to take advantage.
Evans then saw a 40-30 lead slip in the 10th game as Davidovich Fokina set up an all-Spanish quarter-final with Bautista Agut.