The Knight Riders reached 141 for four in pursuit with 17 balls to spare to move to the summit of the IPL log.
Kolkata's slow bowlers dominated for most of the innings, apart from a brief period in the first six overs in which Murali Vijay produced flashes of brilliance. Shaun Marsh was a steady influence throughout with his 56 off 41 balls.
Marsh and Kyle Abbott hammered 18 runs in the final over to steer the Kings XI Punjab to 138 for eight.
The four spinners of the Knight Riders were superb. Sunil Narine was the pick with his 2-22 and Piyush Chawla was another standout-performer with his 1-18. Shakib al Hasan also threatened.
South African fast bowler Morne Morkel took 2-27 and operated well in partnership with Umesh Yadav.
Uthappa and Gambhir struck nine fours in the power play and compiled 65 runs in pursuit of the target of 139.
It was almost atypical T20 scoring in the first six overs. They hardly broke a sweat and played traditional cricket shots to fashion the highest power-play score in this season’s IPL.
Uthappa was the more aggressive of the duo, completing his half-century off 24 balls to power Kolkata.
Pardeep Sahu finally broke the opening stand of 82 when he trapped Uthappa in front for 53.
Glenn Maxwell rewarded Sahu for his crafty efforts with an acrobatic catch at deep cover to remove Gambhir for 34 as the visitors slipped to 98 for two after 11 overs.