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.
After Karthik was stumped, Aaron Finch's hit 29 from 10 balls (3x4, 2x6) before being run out. Ravindra Jadeja sealed the chase with two overs to spare as he launched a six over long-on.
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.
KKR were Stuttering at 24 for 4 inside the Powerplay overs with a splendid seam bowling display by Praveen Kumar (2/19) and Dhawal Kulkarni (1/3), but Pathan and Shakib put on a record unbroken partnership of 134 runs to stage a remarkable recovery.
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.
But Karthik was unfazed and found himself in the zone starting off with three classy boundaries against Brad Hogg.
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 job.
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.
With spin on in the third over, Smith and McCullum unsettled Shakib's rhythm by hitting the left-arm spinner for three boundaries as Lions were off to a brisk start.
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.
Last Updated 31, Mar 2018, 6:59 PM