Opting to bat, KKR rode on Kallis and Manish Pandey's 64 to post a competitive 163 for five, before restricting Mumbai Indians to 122 for seven at the Sheikh Zayed Stadium, with Narine returning match-winning figures of 4/20.
KKR's innings was built on a 131-run second-wicket partnership between Kallis and Pandey.
Pace spearhead Lasith Malinga was the pick of Mumbai bowlers, finishing with figures of 4/23. But the Lankan slinger's effort was not enough, and neither was Ambati Rayudu's 40-ball 48.
Mumbai were off to a subdued start with Morkel not allowing an inch to free their arms. The tall South African pacer was bowling to such an impeccable line and length that even the experienced Michael Hussey had no answer.
More From This Section
The first breakthrough, though, was effected by Narine, who sneaked one through the bat and pad of Hussey. It was a strong comeback by Narine after the Trinidadian's second ball was deposited into the crowd by Aditya Tare (24).
Hussey's departure brought Ambati Rayudu in the middle and giving him company was Tare, who was on the lookout for quick runs.
However, with pressure building up, Tare succumbed when he gave a high return catch to Shakib Al Hasan who held on to it after a fumble.
There was a partnership of 61 runs for the third wicket between Rohit Sharma and Rayudu. But the two fell in quick succession and after that the task was beyond for even the ever-dangerous Kieron Pollard.