Kuldeep Yadav was once again the standout performer for the Delhi Capitals.
In the three overs he bowled, the spinner took four wickets.
Delhi restricted KKR players to 146/9 in 20 overs.
Nitish Rana scored 57 off 34 deliveries to help KKR finish with a respectable total. Shreyas Iyer also contributed a crucial 42 off 37 runs in the middle.
In response, the Delhi Capitals got off to a shaky start in the run chase, losing Prithvi Shaw and Mitchell Marsh in the first two overs.
Warner and Lalit Yadav then put on a solid 65-run stand before Umesh broke the partnership, dismissing Warner for 42.
The Delhi unit was then led home by Rovman Powell, who finished the match with a maximum. He was unbeaten on 33 from 16 balls.