The Spaniard, who dropped just one set on his way to the final, maintained his momentum in the second to outclass Pouille and win his eighth career title.
"This tournament is very special. It is for sure going to be (always) in my heart and I am so happy I have won a 500 event," Bautista Agut said.
"Lucas is a really great player, he has a great future and is playing unbelievable tennis in the last month. I want to wish him good luck for the rest of the season."
Second-seed Pouille, competing in his third ATP final in four events, also lost a chance to move into the top 10 for the first time.
Bautista Agut is expected to climb to world number 16 when the updated rankings are released on Monday.
(Reporting by Aditi Prakash in Bengaluru, editing by Pritha Sarkar)
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