Chasing 159 on a slow Eden surface, the duo of Dwayne Smith (27) and Brendon McCullum (29) handed Lions a perfect launchpad with 42 from 5.3 overs.
The duo fell in space of 15 runs when Shakib Al Hasan and Piyush Chawala took one each but it was sheer elegance from wicketkeeper batsman Karthik who scored a 29-ball 51 that had eight fours and a six to set up the chase.
The Lions thus returned to winning ways after a hat-trick of defeats as they jumped to the top of the table with 14 points from 11 matches, while KKR were pushed to the third behind Sunrisers Hyderabad on net run rate.
Earlier, Yusuf Pathan and Shakib Al Hasan bailed Kolkata Knight Riders out from a disastrous start to post a fighting 158 for four after being invited to bat.
More From This Section
It was highest fifth-wicket stand in IPL history.
Shakib struck a 49-ball 66 with four sixes and as many fours while Pathan came up with a 41-ball 63 that had seven shots to fence and one over the ropes.
72 runs were needed from 60 balls when a dangerous-looking McCullum, having struck two sixes and one boundary in the previous over, fell to Chawla as KKR were attacking full force with their spin trio.
First he reverse swept Hogg to thirdman, then guided with the spinner to long on and displayed a fine flick off the wrist for a third boundary.
Raina on the other hand looked ordinary before getting dismissed to another short ball when he was caught by Hogg but it did not matter as Aaron Finch (29 off 10) did the jiob smartly before being run out.
McCullum found himself lucky to be adjudged not out when he took an outside edge from Andre Russell in the first over but he survived to open his account and give their chase the fillip with equally devastating Dwayne Smith.
Smith slammed Shakib over square leg in his next over but only to be foxed by a slower one in the next ball as KKR got their first breakthrough.