Gambhir (60) anchored the 152-run chase with his 47-ball knock as he and fellow opener Robin Uthappa (46) rattled up a 100-run stand, which paved the way for an easy win, which was 11th in a row for the IPL champions in this format.
The chase was complete in 19.3 overs as KKR lost five quick wickets after being placed comfortably at 113 for one at one stage.
Narine scalped two batsmen in two balls in his three-wicket haul and it was largely the contributions from opener Ahmed Shehzad (59) and Umar Akmal (40) that propped up the Lions innings.
Gambhir and Uthappa stroked freely before off-spinner Adnand Rasool broke the stand by castling the latter in the 13th over. Exactly 12 balls later, Gambhir met the same fate at the hands of paceman Mustafa Iqbal.
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KKR were firmly in control at that stage but lost wickets in a heap after that as they lost Manvinder Bisla (6), Yusuf Pathan (11), Ryan ten Doeschate (12) and Andre Russell (1).
Gambhir was hardly troubled by any Lions bowlers as they bowled either full or short-pitched stuff at the Indian batsman, who got better and better with each stroke.
Gmabhir had no problem whatsoever as he and KKR were off to a flying start. The southpaw played ferocious cuts when challenged with short balls, lofted confidently on full length balls and dabbed elegantly as KKR raced to 48 in six overs.
Uthappa was dropped on 14 when the fielder failed to hold on to a difficult chance off paceman Cheema. This was after Uthappa drove Cheema for two boundaries.
Uthappa lofted Mustafa Iqbal for a six and a four as KKR were placed comfortably and in control at 82 for none at half-way mark. He though encountered cramps in the middle of the 11th over and received treatment from physio.