Nair anchored the Rajasthan's run-chase with 50-ball 73-run innings which was laced with eight boundaries and two sixes. The 22-year-old added 51 runs off 43 balls for the second wicket with Sanju Samson (34) as Royals overhauled the 153-run winning target with nine balls to spare.
Earlier, opener Quinton de Kock blasted 43 off 33 balls at the top, while JP Duminy provided the late charge with a 31-ball 39 to power Delhi Daredevils to a competitive 152-5 in their stipulated 20 overs after Rajasthan skipper Shane Watson won the toss and elected to field.
Defending 152, Wayne Parnell dismissed Ajinkya Rahane (12) early in the innings with Murali Vijay pulling off a sensational catch at cover. But the early setback didn't affect Rajasthan's run chase as other opener Nair and Sanju Samson (34) stitched together 51 runs off 43 balls for the second wicket.
But their promising partnership was cut short by spinner Shabhaz Nadeem off the last ball of the 10th over when he deceived Samson with a tossed up delivery and wicketkeeper Dinesh Karthik did a good job behind the wicket to reduce Rajasthan to 71 for two in 10 overs.
Samson hit two boundaries and a couple of sixes in his 28-ball innings.
Rajat Bhatia then joined Nair and the duo picked up sixes off Unadkat and Rahul Sharma over extra cover and long on respectively as Rajasthan crossed the 100-mark in the 13th over.
Bhatia was dismissed by Mohammed Shami in the 15th over. But it didn't have any affect as Watson (16) and Nair then finished the job with an unbeaten 41-run partnership off only 21 balls.
For Delhi, Parnell, Nadeem and Shami took one wicket each.