Unadkat (3/15 off 4 overs) dismissed Prithvi Shaw, Shikhar Dhawan and Ajinkya Rahane to trigger DC's top-order collapse from which they never recovered fully.
Captain Rishabh Pant's blistering 32-ball 51, studded with nine fours, was not enough as DC could only post a modest total after being put in to bat.
DC made a disastrous start as they were two wickets down for 16 runs in the fourth over with Unadkat dismissing the opening duo of Shaw (2) and Dhawan (9) cheaply.
Shaw was the first to go in the second over, caught at backward point before Dhawan perished while attempting a ramp shot with RR captain and wicketkeeper Sanju Samson taking a stunning diving catch to his right.
Ajinkya Rahane's (8) underwhelming IPL form continued as he offered an easy caught and bowled chance to Unadkat with a slow ball that clocked just 110km per hour.
DC were 36 for 3 at the end of power-play but the slump continued as Marcus Stonis (0), foxed by a Mustafizur Rahman (2/29) delivery, checked his shot at the last minute to offer a running catch to Jos Buttler.
The run rate started increasing once captain Pant came to the crease but still DC were 57 for 4 at the halfway mark.
Once he had a full measure of the pitch, Pant opened up and hit four boundaries, three of which were consecutive, to take 20 runs from the 11th over bowled by Rahul Tewatia.
Pant, in excellent form this year, reached to his fifty off 30 balls in the 12th over, with a four off Mustafizur but he was run out the next over with bowler Riyan Parag's throw crashing onto the stumps.
Delhi were 88 for 5 then. After Pant's exit, Tom Curran gave some respectability to the DC innings with a 16-ball 21.