Defending champion Andy Murray is through to the last 16 at Wimbledon after a 6-2 6-3 6-2 win against Spain's Roberto
The Spanish 27th seed had been expected to provide Murray's first test but the defending champion was even more impressive than he had been in the first two rounds.
Murray's coach Amelie Mauresmo will no doubt be delighted with their first week of grand slam tennis, and the pair will now have two days to prepare for a fourth-round meeting with big-serving Kevin Anderson.
Murray had looked extremely good in defeating David Goffin and Blaz Rola in his first two rounds but this was undoubtedly a step up.
Bautista Agut may not be a household name but he is having the best season of his career and last week won a title on grass in Holland.
As Murray had pointed out before the match, the Spaniard hits the ball a lot flatter than most of his countrymen, making his game well suited to the faster surfaces.
He certainly had no trouble settling into his first match on Centre Court, winning the opening six points and engaging his opponent in lengthy rallies.
But Murray is a master at point construction and showed off all his grass-court wiles to break for 2-1.
Even when he seemed in trouble, he had the answer, flicking a forehand cross-court winner on the run beyond Bautista Agut to bring up three break points and then taking the first.
Murray was being watched from his player box by comedian Ricky Gervais but he was all business on the court, breaking the
Spaniard again to lead 5-2 and then serving out the set to love.
One thing Bautista Agut does not possess is a big serve and the lack of free points was hurting him badly.
It took only three games of the second set for Murray to break through again, Bautista Agut ending another long rally by over-pressing with his forehand.
Murray's serve was working beautifully while the rest of his game was not bad either, and a forehand curled well beyond the reach of Bautista Agut gave him a 5-2 lead.
Serving for the set he had a slight lapse and dropped serve for the first time all tournament.
He immediately brought up three set points on his opponent's serve, only to miss backhands on each one.
But a searing forehand created a fourth and this time he took it with the cutest of backhand drop volleys.
Having allowed matches to become unnecessarily long and complicated at the French Open, Murray has been determined to keep his foot firmly on the accelerator pedal here.
And after only eight minutes of the third set he was already 3-0 up, breaking the Bautista Agut serve for a sixth time with a sweetly-struck backhand.
Murray has cut the calm and authoritative figure befitting a defending champion, celebrating each step forward with understated fist pumps.
There was another one when he made it five games in a row, only for Murray to then double fault twice to hand his opponent a second break.
Just for a moment it looked like Bautista Agut might get the set back on serve but Murray stamped out the danger with some more big serving.
There were plenty of highlights to delight the evening crowd on Centre, not least an impudent backhand winner that brought up a first match point.
That went begging, as did two more, but on the fourth chance Bautista Agut put a forehand long, Murray wrapping up a thoroughly convincing win after an hour and 36 minutes.
Rolling around in pain clutching his left shoulder, Novak Djokovic's Wimbledon hopes looked in serious jeopardy against Gilles Simon on Centre Court on Friday but he recovered to win 6-4 6-2 6-4 and reach the last 16.
Leading 3-2 in the third set the Serb was closing in on an uneventful victory against his French opponent when he stumbled and dived to reach a forehand, crashing heavily to the turf.
With the 2011 champion apparently in extreme pain and with concerned coach Boris Becker watching on, it looked as though Djokovic might not be able to continue but after walking to his chair where a trainer manipulated his shoulder, he carried on.
Despite looking a little tentative, he showed no obvious signs of discomfort and finished the job with a smash.
Djokovic will now get the weekend to recover from his fall before playing 14th seed Jo-Wilfried Tsonga of France in the fourth round.
Djokovic said he had called for medical attention on court for reassurance he had not damaged his left-shoulder joint.
"I thought it was an awkward fall, I was just hoping there was nothing bad going on with the joint," he said.
"Luckily there's no damage in the joint, I could play a few games after that and just the muscle was quite sore because of the impact.
"But all in all I'm just very glad to get through."