Five-time champions Chennai crashed to their fifth defeat in a row, leaving the fans mighty disappointed.
The total was Chennai's lowest at their home ground Chepauk and the third-lowest ever in the IPL.
Kolkata are now third in the points table with Chennai languishing in ninth position in the 10-team competition.
"We had our plans and that worked well for us," said Kolkata skipper Ajinkya Rahane.
Openers Quinton de Kock and Narine gave Kolkata a flying start before Chennai got a breakthrough in the fifth over.
Medium pacer Anshul Kamboj sent De Kock back for a 16-ball 23 but Narine carried on with aplomb.
Narine hit Ravichandran Ashwin for two sixes on the trot and by the time he was bowled by Noor Ahmad, victory was well within the sight of Kolkata.
"We need to look deep down inside. Challenge was there, but we needed to tackle," said Chennai skipper Mahendra Singh Dhoni.
"We didn't have enough runs on the board."
Put in to bat, Chennai lost their openers Devon Conway and Rachin Ravindra early, with just 16 runs on the board.
Chennai could have been in deeper trouble but Narine dropped a sitter at mid-off, offering a reprieve to Vijay Shankar.
Shankar, who was dropped again on 20 by Venkatesh Iyer at midwicket, went on to make 29 off 21 balls with two fours and a six.
Rahul Tripathi, coming into the squad in place of the injured Ruturaj Gaikwad, was bowled by Narine for 16 to leave Chennai tottering at 65/4.
The rest of the Chennai order buckled under the pressure, making their way back to the pavilion without making any impact.
Dhoni, named skipper Thursday after Gaikwad was ruled out of the rest of the season, also failed to weave his magic, trapped leg before for one off Narine (3/13).
Shivam Dube, hit an unbeaten 31 off 29 balls, to take the side past the 100-run mark.
25TH MATCH
Chennai Super Kings 103/9 (Dube 31*, Narine 3/13) lost to Kolkata Knight Riders 107/2 in 10.1 overs (Narine 44, De Kock 23) by 8 wickets
END/MSS/AJ
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