Bautista-Agut drew first blood by breaking his opponent's serve at the first time of asking, but Berdych broke back instantly to level proceedings.
Bautista-Agut almost saved five break points to keep himself in contention, but Berdych nabbed the game and a further break point to push on and take a one-set lead.
Berdych continued his dominance by grabbing an early break in the second set, and despite Bautista-Agut's attempts to draw level on sets, it was the 28-year-old who doubled his lead on the clay court.
After a delay due to rain, both competitors pushed the third set into a tie-break after grabbing a break apiece in the third set.
Despite some impressive shots from Berdych, it was Bautista-Agut who forced the match into a fourth set, but he was unable to continue his momentum.
Berdych grabbed an early break of serve, and despite losing one of his own service games, he was able to bounce back to wrap up the contest.