De Kock blasted 43 off 33 balls, which was studded with five fours and a six, while Duminy smashed 39 off 31 balls, laced with four fours and one six, after Delhi were asked to take first strike by Rajasthan Royals.
Kedar Jadhav's cameo of 28 from 14 balls helped them cross the 150-run mark.
For Rajasthan, James Faulkner (2/26) and Pravin Tambe (2/25) were the prime performers.
Young De Kock did most of the scoring in the Powerplay, blasted three fours and a six over the leg side boundary as Delhi were 46-1 in six overs.
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Skipper Kevin Pietersen too should have been back in the hut as he was found short by a throw from wicketkeeper by in the first ball of seventh over by Rajat Bhatia. But on-field umpire Sanjay Hazare didn't refer it to the third umpire, thus giving Pietersen a respite when he was on 2.
De Kock, who was playing well so far at the other end, too ended up giving a simple catch to Tambe on the last ball as Delhi slipped to 72 for three in 10 overs.
The twin strike by Tambe brought two newman -- Dinesh Karthik and JP Duminy -- at the crease and they tried to steady the ship with a 24-run stand in 32 balls.
Faulkner was the one who broke the stand when he had Karthik, hole out to Stuart Binny at deep square leg in the 16th over.