Duminy smashed 40 off 28 balls while Jadhav blasted 26 off 15 in their 55-run unbeaten stand, providing the necessary impetus in the end.
Electing to bat, Delhi did not have the best of starts as the Kolkata think-tank changed bowlers at either ends to bottle up the flow of runs even as Quinton de Kock got a couple of boundaries.
KKR opened the bowling with off-spinner Suryakumar Yadav, who shared the new ball with Jacques Kallis. Umesh Yadav drew first blood for Kolkata in the third over, getting De Kock caught by Gautam Gambhir at mid-on for 10.
Murali Vijay (24) and Dinesh Karthik (36) then tried to stabilise the innings as KKR continued to juggle their bowling options. The duo added 31 runs for the third-wicket as both the batsmen mixed the right dose of caution and aggression to give some momentum to the Delhi innings.
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Trying to push the scoring rate, Vijay finally holed out a simple catch to Sunil Narine at long on as Kallis got his first wicket.
Kallis though got his revenge when he caught the Delhi batsman in the very next over off Shakib al Hasan for 36.
The over-ambitious Karthik tried the paddle scoop again only to top edge the ball to short fine leg.
Laxmi Ratan Shukla and Duminy did try to up the ante but clinical bowling from Umesh and R Vinay Kumar kept the batsmen in check even in the middle overs.
Laxman's exit though proved a blessing in disguise for Delhi as new man Jadhav smacked a four and a six off Vinay to provide some entertainment to the Kotla crowd.
Duminy and Jadhav entertained the crowd with fours and sixes as they managed to notch up a run-rate of over 13 in the final four overs.