KKR skipper Gautam Gambhir led the way with 69 as the visitors snapped a four-match losing streak by chasing down 161 with 10 balls to spare.
Kevin Pietersen's side slipped to their sixth defeat in eight with the out-of-touch skipper making just six in his side's 160-5 at the Feroz Shah Kotla.
Pietersen won the toss and chose to bat, but Delhi managed just 29 in the powerplay with the discarded England batsman involved in a disastrous run out with opener Murali Vijay.
Vijay made 24, while Dinesh Karthik contributed 36 before JP Duminy and Kedar Jadhav gave the tail end of the innings some vigour.
South African Duminy hit three sixes in making 40 from 28 balls while Jadhav added 26 from 15.
|Delhi Daredevils: 160-5 (20 Overs)|
|Quinton de Kock||c Gautam Gambhir b Umesh Yadav||10||9||111.11||2||0|
|Murali Vijay||c Sunil Narine b Jacques Kallis||24||20||120.00||2||1|
|Kevin Pietersen||run out (Robin Uthappa)||6||12||50.00||1||0|
|Dinesh Karthik||c Jacques Kallis b Shakib Al Hasan||36||22||163.63||4||1|
|JP Duminy||NOT OUT||40||28||142.85||0||3|
|Laxmi Ratan Shukla||b Sunil Narine||10||14||71.42||1||0|
|Kedar Jadhav||NOT OUT||26||15||173.33||3||1|
|EXTRAS||(w 2, lb 6)||8|
|Shakib Al Hasan||4||0||13||1||3.25||12|
However, that total soon looked insufficient as Robin Uthappa and Gambhir put on 106 for the opening wicket in Kolkata's reply.
Uthappa went for 47 in the 12th over but Gambhir, who started the tournament with just one run from his first four innings, went on to complete his second consecutive half-century.
He hit five boundaries and two sixes in his 56-ball innings before becoming Wayne Parnell's second victim with his side just 10 runs short of their victory target.
However, Jacques Kallis and Manish Pandey saw them over the line.
|Kolkata Knight Riders: 161-2 (18.2 Overs)|
|Robin Uthappa||lbw Wayne Parnell||47||34||138.23||5||1|
|Gautam Gambhir||c Dinesh Karthik b Wayne Parnell||69||56||123.21||5||2|
|Manish Pandey||NOT OUT||23||14||164.28||2||0|
|Jacques Kallis||NOT OUT||10||6||166.66||2||0|
|EXTRAS||(w 1, lb 11)||12|
|Laxmi Ratan Shukla||2||0||19||0||9.50||2|
Kolkata join Royal Challengers Bangalore on six points in fourth place in the standings.