Asked to bowl, KKR first restricted Delhi Daredevils to 168 for eight and then chased down the target with one ball to spare, reaching 169 for six.
Pandey steered the KKR chase with a 49-ball unbeaten 69, a knock that was laced with four boundaries and three sixes.
Besides Pandey, Yusuf Pathan made useful 59 off 39 deliveries with the help of six boundaries and two hits over the fence.
For Delhi Daredevils, skipper Zaheer Khan (2/28) and Pat Cummins (2/39) impressed with the ball.
Kolkata Knight Riders:
Gautam Gambhir c Mathews b Zaheer 14
Colin de Grandhomme c Billings b Khan 1
Robin Uthappa c Pant b Cummins 4
Manish Pandey not out 69
Yusuf Pathan c & b Morris 59
Suryakumar Yadav c Khan b Cummins 7
Chris Woakes st Pant b Mishra 3
Sunil Narine not out 1
Extras: (LB-3, W-8) 11
Total: (for 6 wickets in 19.5 overs) 169
Fall of wickets: 1-5, 2-19, 3-21, 4-131, 5-152, 6-160
Bowling: Zaheer 4-0-28-2, Cummins 4-0-39-2, Morris 4-0-30-1, Mishra 2.5-0-26-1, Shami 3-0-28-0, Mathews 2-0-15-0.