The second seeded Serb came back strongly after losing the first set to beat the 80th-ranked Agut 3-6, 6-1, 6-3 in an hour and 49 minutes at the Nungambakkam tennis stadium.
Tipsarevic conceded just four games in the last two sets to end the giant-killing run by the 24-year-old Spaniard, who defeated top-seed Tomas Berdych in the quarter-finals.
Tipsarevic won the Chennai title for the first time after five unsuccessful attempts, including a loss to big-serving Canadian Milos Raonic in last year’s final.
“I am extremely proud of finally winning in Chennai,” Tipsarevic said. “I just love this place and was desperate to win. It also gives me just the start I need for the season. To be fair to Roberto, I did not play my best tennis. I was too passive in the first set and waited for him to make mistakes. But I am happy I was mentally stable and came back in the final two sets.”
Asked if his next goal was the Australian Open title, Tipsarevic said he was realistic enough. “Men’s tennis is tougher than ever before. It’s not easy to beat the top players. To win a Grand Slam, I will have to beat at least three of the top four. I hope I can achieve that some day.”