Tsitsipas' first grass-court title on the ATP Tour comes before Wimbledon starts Monday.
The second-seeded Greek held off a late rally in the decisive set to beat Bautista Agut 6-4, 3-6, 7-6 (2) for his tour-leading 40th win of the season.
His ninth career title was also Tsitsipas' second of the season after he retained his Monte Carlo title in April.
Tsitsipas, sixth in the rankings, has drawn Alexander Ritschard of Switzerland in the opening round of Wimbledon.
Bautista Agut was trying for his second title of 2022 as well and to add to his 10 career titles. He will face Attila Balazs in the first round at Wimbledon.
Tsitsipas appeared to be cruising in the third set after getting an early break to open up a 4-1 lead. But 20th-ranked Bautista Agut, who upset top-ranked Daniil Medvedev in the quarterfinals, broke Tsitsipas when he was serving for the win and forced the tiebreaker.