Put into bat, DD were hurt by lack of partnerships but a late flourish from Angelo Mathews (21-ball 28) helped the home side get some respect to their total as Morkel and Yadav picked two wickets apiece.
The South African pacer (2-30) drew first blood after getting Mayank Agarwal (1) caught at long leg with Umesh Yadav taking a sprawling catch.
Mystery spinner Sunil Narine then struck in his very first over, cleaning up skipper Jean-Paul Duminy (5), who was done in by an off-spinner that was pitched outside the leg-stump to the left-hander.
Just when it seemed the Mumbai-born player, who hit 3 fours and a six, is ready to take on the KKR bowlers, leg-spinner Piyush Chawla got the dangerman cleaned up in the ninth over.
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Tiwary then joined hands with Yuvraj Singh (21) to not only rebuild the DD innings after the strategic time out but also improve the scoring-rate with a few hits to the fence.
But the Bengal player, whose 28-ball stay was laced with 5 fours, was scalped by Morkel after he mis-timed a pull to short mid-wicket as the fourth wicket 37-run partnership came to an end.
KKR bowlers continued to hurt the DD batting after Umesh Yadav got Kedar Jadhav (12) caught at backward point on the last ball of his third over.
But Mathews got stuck into Narine, hitting the off-spinner for two consecutive sixes and ended the 19th over with a boundary to get 20 runs of the West Indians' final over.
Earlier, the two teams also observed two minutes silence in memory of young Bengal player Ankit Keshri, who died of a cardiac arrest three days after sustaining head injuries post a freak on-field collision during a CAB one-day game.