The Titans, reigning IPL champions, looked to have wrapped up victory after Afghanistan spinner Rashid Khan claimed a hat-trick to leave Kolkata reeling at 155-7 in the 17th over.
With Kolkata needing 29 runs off the final over, Yash Dayal was handed the ball and after Umesh Yadav took a single off the first delivery, Rinku cut loose.
The 25-year-old capitalised on three full tosses to clear the ropes before smashing the final two balls from outside off stump over the long-on boundary as Kolkata won by three wickets.
“I was just trying to hit sixes. I was not thinking a lot, was just reacting to the ball,” said Rinku, who was named player of the match.
“It kept coming out of the middle, I had belief and it came off in the end.”
Rinku set a record for most runs by any batter in the 20th over of an IPL run-chase. “Rinku played unbelievable shots and credit goes to him for the way he played and for the way he finished,” Titans captain Rashid said.