Earlier, Zaheer Khan, the DD skipper won the toss and decided to field first, managing to restrict the Punjab side to a modest 111 runs.
The Delhi bowlers picked up 9 wickets, with Amit Mishra wreaking havoc upfront.
The leg spinner picked up four wickets, while giving away just 11 runs in his three overs.
Zaheer Khan, Chris Morris and Jayant Yadav accounted for a scalp each.
The Kings had a torrid start as Murali Vijay departed for 1, while the score board read eight runs for the loss of one wicket.
Manan Vohra (32) top scored for his side, but the others failed to convert their start.
Shaun Marsh (13), David Miller (9) and Glenn Maxwell (0) each fell prey to Mishra.
Important contributions from Mohit Sharma (15) and Pradeep Sahu (18 not out) helped their team cross the 100-run mark
Chasing the score, Delhi lost Shreyas Iyer (3) early for just 9 runs, but a 91-run partnership for the ensuing wicket from Quinton de Kock and Sanju Samson sealed the game for them.
Though Samson perished for 33, trying to smash Axar Patel for a maximum, de kock remained unbeaten.
The South African hit nine fours and a six in his knock of 59 runs.
Pawan Negi, who walked in at number four, ended proceedings with a six.
Mishra was adjudged the Man of the match.
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