Quentin de Kock and Murali Vijay began briskly for Delhi, putting up 99 off 11.1 overs before KV Sharma removed de Kock.
From there on, things became tougher for the Delhi Daredevils as Kevin Pietersen, playing his first game of the tournament, struggled to get the ball off the square.
Murali Vijay departed in the 13th over and after that, Dinesh Karthik too was not able to keep up with the required run rate of over 9 runs per over.
Karthik and Pietersen finally got a few boundaries, but Dale Steyn came back in the 17th over to remove both off successive deliveries, even as the two attempted to procure some big hits to keep up with the increasingly difficult task.
JP Duminy and Manoj Tiwary then attempted to score 50 off the last 19 deliveries. Tiwary smashed Amit Mishra for a six in the 18th over and Duminy followed suit in the same over. Mishra's over went for 18 runs overall.
The next over bowled by Steyn was also plundered for two boundaries, but it still left Delhi needed 20 off the last over.
With 13 runs needed off two balls, Duminy tonked Bhuvaneswar Kumar for six, but could not repeat the feat the next ball, thus leaving Delhi 4 runs short.
Batting first, Sunrisers reached 184/1 in 20 overs. The only wicket to fall was of Shikhar Dhawan, who scored a brisk 33 off 22 balls before holing out to Kevin Pietersen.
The first wicket partnership between Dhawan and Aaron Finch made 56 off 6.2 overs.
Finch and David Warner then took on the mantle of scoring quickly, and never relinquished it. Finch scored 88 and Warner 58 as Sunrisers finished on 184/1.
In the end, it proved to be just enough.