Narine was the pick of the bowlers scalping four wickets conceding just 13 runs with an economy of 3.75 in his four overs.
Captain Gautam Gambhir top scored with 42 runs and compiled crucial 47-run partnership with Jacques Kallis as KKR chased 128 in 18.4 overs.
Shahbaz Nadeem was the pick of the bowlers for Delhi Daredevils scalping two wickets and conceding 22 runs off his four overs.
Manoj Tiwary too chipped in with a handy 23 compiling 41-run stand with Gambhir.
Sunil Narine was adjudged the man of the match for his miserly bowling spell of 4-0-22-4.
Captain Mahela Jayawardene waged a lone battle top scoring with 66 as wickets fell around him at regular intervals.
Delhi Daredevils were off to a terrible start as opener Unmukt Chand was cleaned up by Brett Lee on the first ball of the match.
After Chand's wicket, David Warner and Mahela Jayawerdene steadied the Delhi innings with a 44-run stand before Warner was picked up by Sunil Narine.