Daredevils batsmen fired in unison as they chased down the target of 186 with five balls to spare at the Feroze Shah Kotla here.
Corey Anderson top-scored with an unbeaten 41 from 24 balls with the help of two fours and three sixes as Daredevils
Reached 189 for 4 in 19.1 overs.
All other Daredevils batsmen chipped in. Sanju Samson (24), Karun Nair (39), Rishabh Pant (34), Shreyas Iyer (33) and Chris Morris (15 not out) made handy contributions.
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With the win, Daredevils jumped to sixth spot with six points from nine matches while Sunrisers remained at third with 13 points from 11 games.
Earlier, Daredevils managed to choke Sunrisers in the middle overs but Yuvraj Singh's splendid fireworks late in the innings led the defending champions to a challenging 185/3.
Sanju Samson dropped Yuvraj on 29 and the dashing left- hander exploited it to hit his second fifty of the season. After making 62 against RCB in his first match, he was struggling for runs and he found touch when the team needed.
In the last three overs Sunrisers collected 52 runs with Kagiso Rabada leaking 39 runs in 18th and 20th overs.