Uthappa, who was last season's top run getter in their winning IPL triumph, hit his first half-century this season.
Fleming joked that a total of 350 was looking imminent.
Defending a modest target of 135, Bravo was given the ball in the final over with KKR requiring 17 runs to win.
It is no secret that bowling has been KKR's main strength.
Kolkata Knight Riders will look to take avenge for their two run-defeat against Chennai Super Kings.
Led by Ashish Nehra and Ishwar Pandey, CSK's bowling arsenal has looked well equipped.