The number two seed and last year's finalist Tipsarevic lost the first set but found his rhythm back to beat the unseeded 24-year old in a first-time meeting.
The 28-year-old Tipsarevic, who lost to Milos Raonic in last year's marathon final in Chennai, won his fourth career ATP World Tour title in timely fashion with the Australian Open just over a week away.
"I think there's just one word to say and it's 'finally'," he said after winning his first title in Chennai in his sixth attempt.
"Last year, some of you may know, I could smell it, it was just there."
Bautista-Agut, who defeated top seed Tomas Berdych in the quarter-finals, looked set for his first title at one stage but Tipsarevic fought back brilliantly to wrest control, exactly like he did against Aljaz Bedene of Slovenia in the semi-final.
"Roberto was the just the better player than me in the first set, making me move left and right and being the dominant man on court," Tipsarevic said during the prize distribution.
"But I refocused, similar to my semi-final, and I took it step by step from there."