Just weeks after defeat to another compatriot, Rafael Nadal, in the French Open final, the 31-year-old came out on top in what was just the 10th all-Spanish men's singles clash played on the All England Club turf.
It was by no means easy for Ferrer. Looking rusty, he was made to work by the world number 60 and took just under three hours to win through 6-3 3-6 7-6 (7/4) 7-5 on Court One.
Originally slated for Thursday, the match finally got under way at 1353 BST on Friday and it did not take Ferrer long to break serve for a 2-0 lead in the first set.
Rather than buckle, big-hitting Bautista Agut struck back immediately and was unsettling his compatriot by mixing baseline shots with drop shots.
There were some incredible rallies as the rain clouds threatened a downpour, but it did not come as Ferrer broke again en route to taking a tough first set in 43 minutes.
The second began in the same vein, with Bautista Agut proving a difficult opponent in an even contest.
The 25-year-old did well to hold serve in the third game of the second set and broke for 5-3 after a Ferrer double fault.
It allowed Wimbledon debutant Bautista Agut to earn parity but he was only level for 51 minutes.
It took a tie-break to settle a topsy-turvy third set in which both players failed to dominate the serve, with Ferrer eventually coming through victorious.
Bautista Agut returned strongly despite requiring attention on several occasions, only to be broken in the 11th game of the fourth set as Ferrer set up a third-round tussle against Alexandr Dolgopolov, a match which will take place on Saturday.
Ferrer said: "I am happy because we finished the match and I won the match.
"It was a very, very tough match. Roberto is a very good player and he played a very good match. It was very close.
"I feel good, I feel better than the first day and last week. Every day I am improving my game on grass court and now I am in the third round so I am good.
"The third round is going to be a very difficult match. He is a very good player.
"He plays very flat with his serves, is a very good talent, so I need to play like today.''