After restricting the Daredevils to a meagre score of 114 for eight, Sunrisers chased down the total in 19.2 overs, scoring 115 for seven.
With the win, Sunrisers go second in the table, joint on six points with table toppers Royal Challengers Bangalore, while Delhi languish at the bottom with zero points.
A lot was expected from Virender Sehwag's return but it all went sour for the Daredevils from the first over of the match itself.
Electing to bat, Delhi lost their Australian import and their top scorer this year, David Warner (0) to Dale Steyn's fourth ball of the match.
That set the trend for the rest of the innings as the Daredevils lost wickets at regular intervals.
Skipper Mahela Jayawardene (12) looked in sublime touch, first hoicking Ishant Sharma for a six over the square leg boundary and then caressing compatriot Thisara Perara through extra cover.
But his innings was shortlived as he skied an Ishant Sharma ball straight to the waiting hands of the mid-on fielder.
Sehwag (12), who had struck two boundaries in his innings, departed two balls later, edging Ishant to the wide-slip catcher, Cameron White.
Johan Botha (9) and Manpreet Juneja (15) failed to impress as Delhi found themselves in heaps of trouble with the score on 65 for five.
Irfan Pathan (15) and Kedhar Jadhav (30 not out) brought about the innings best partnership with 30 runs but the former was dismissed in his zeal to score quick runs.
Jadhav's cameo was the saving grace for the Daredevils as he plundered Sri Lankan all-rounder Thisara Perera for 13 runs in the last over, taking Delhi to a respectable total.
In reply, the Sunrisers too got off to the worst possible start, losing Akshath Reddy (1) in the second over.
Parthiv Patel (19) and Kumar Sangakkara (28) added 44 runs for the second wicket as it seemed the visitors would easily canter to victory.
Patel though was too eager to score quick runs on a slow wicket and that proved to be his downfall as he lobbed an easy catch to spinner Shahbaz Nadeem.
But it was Sangakkara's wicket that reignited Delhi's hope with the former Sri Lankan captain edging a Botha delivery to Sehwag at first slip.
Jadhav stumped White (4) off Nadeem's bowling while Hanuma Vihari (17) fell to Morne Morkel as Delhi were well and truly in the game.
Amit Mishra, though, had the last say in the game as his unbeaten 16 took the Sunrisers over the line.
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