The world number 24 claimed a ninth ATP Tour title on Saturday with a 6-4 3-6 6-3 victory in just under two hours.
Spaniard Bautista Agut, the tournament's seventh seed, forced a break chance to lead 5-3 midway through the opening set, which he eventually claimed while Czech Berdych saved three set points on his next service game.
Berdych, ranked 71st in the world, had beaten Italian fourth seed Marco Cecchinato to make the final and would go on to force a decider having moved 3-1 ahead in the second set.
Bautista Agut, though, again found his range when it mattered to break Berdych early on and then move 5-2 up before closing out victory on his first match point with a love service game.
At the Tata Open Maharashtra in Pune, top seed Kevin Anderson defeated veteran Ivo Karlovic 7-6 (4) 6-7 (2) 7-6 (5) to claim his sixth tour-level title.
The South African had found himself 5-2 down in the deciding tie-break but fought back to win the ATP Tour final in the open era contested by the two tallest players.
Croatian Karlovic, the 39-year-old standing at 6ft 11ins, had also made history as the oldest player since Ken Rosewall, aged 43, at the 1977 Hong Kong Championship to reach a tour-level final.
"You don't get to win tournaments every week, so when you do it is very special and it is something that definitely means a lot to me," Anderson said at the trophy ceremony, reported by the ATP Tour's website.
Second seed Kei Nishikori will take on Daniil Medvedev in Sunday's final of the ATP Brisbane International.
Japan's world number nine beat Jeremy Chardy of France 6-2 6-2, while Russian Medvedev saw off Jo-Wilfried Tsonga 7-6 (6) 6-2.
