Kolkata won the toss and chose to field, removing the dangerous Dwayne Smith for just five runs with the eighth ball.
Chennai had number three Suresh Raina (65) largely to thank for their 154-run total - the Indian built partnerships with Brendon McCullum (28), Faf du Plessis (23) and MS Dhoni (22) before he fell to Piyush Chawla in the 18th over.
Kolkata lost just two wickets as they reached 156 with two overs to spare.
Uthappa led from the front, hitting several early boundaries on his way to 67 before he lost his wicket to Ravindra Jadeja in the 12th over.
The Super Kings have already qualified for the playoffs in second, but the Knight Riders are now just two points behind them in fourth.