Daredevils got the bulk of their runs through openers Mayank Agarwal (37 in 21 deliveries) and Shreyas Iyer (40 in 30 balls). Skipper Jean-Paul Duminy (not out 44), Yuvraj Singh (27 runs in 17 balls) and Angelo Mathews (not out 27 in 14 balls) provided the late spark.
Agarwal got the Daredevils off to a flying start as he cracked 37 in just 21 deliveries. His knock included six fours and one six.
The Karnataka right-hander attacked the Royals pace bowlers. After showing his intent with a daring pull off New Zealander Tim Southee, he followed it with a flick off Chris Morris in the second over.
When Southee returned, Agarwal got onto the front foot and drove over the cover boundary for a six.
Royals stand-in-skipper Steven Smith removed Morris and brought in Dhawal Kulkarni and the Mumbai pacer was treated with similar disdain. Agarwal collected four fours that helped Daredevils score 44 runs in only four overs.
However, leg-spinner Pravin Tambe pulled the plug on Agarwal's innings with the batsman offering a return catch to the bowler.
After a couple of quiet overs, Iyer blasted Tambe for a six and a four towards the long-on boundary before offering a catch to Southee off Morris. Iyer made 40 in 30 deliveries.
At 93/2 after 11 overs, 2015 IPL's costliest buy Yuvraj -- at Rs.16 crore -- joined Duminy in the middle.
Yuvraj perished after scoring a 17-ball 27. Ace Sri Lankan all-rounder Mathews, who was picked in the XI ahead of in-form Albie Morkel, justified his selection as he fired 27 in 14 balls.
Along with Duminy, Mathews and Yuvraj ensured that Daredevils posted a challenging total.
Brief scores: Delhi Daredevils 184/3 in 20 overs (Jean-Paul Duminy not out 44, Shreyas Iyer 40, Mayank Agarwal 37; Chris Morris 2/35) against Rajasthan Royals.