Chasing 129 for victory, KKR reached the target by losing only four wickets and with eight balls to spare.
Skipper Gautam Gambhir remained the top scorer for the home side with his 42 runs. He hit five boundaries and six in his 29-ball innings.
KKR failed to make a good start to their innings as they lost the wicket of Manvinder Bisla (4) in the second over. His wicket was picked up by Delhi's Ashish Nehra.
Kallis (23) and Gambhir added crucial 47 runs in the second wicket partnership.
Local lad Manoj Tiwary contributed 23 runs with his willow.
Eoin Morgan (14*) and Yusuf Pathan (18*) remained not out till the end of the innings and ensure KKR the first victory in the tournament.
Shahbaz Nadeem remained the pick of the Delhi bowlers as he picked up two wickets by giving away 22 runs in his four overs.
Earlier, Delhi Daredevils were bundled out for 128 all out in 20 overs.
Skipper Mahela Jayawardene remained the top scorer for the visitors with his 66 runs. He hit eight boundaries and a six in his innings.
David Warner (21) was the only other batsman to post a double-digit score in Delhi's innings.
KKR's spinner Sunil Narine bowled brilliantly and picked up four wickets by giving away 13 runs in his four overs.
He was declared the man of the match.
--IBNS (Posted on 04-04-2013)