Chasing 185 for a win, Royals rode on Hooda's 25-ball 54 to achieve the target on the last ball of the innings.
Put into bat, Delhi rode on a 45-run opening start by Mayank Agarwal (37) and Shreyas Iyer (40) to post a challenging 184 for three in 20 overs.
But even on a day that belonged to the 19-year-old Hooda, Delhi spinner and man-of-the-match Imran Tahir made his presence felt with a four-wicket haul.
Delhi leg-spinners Tahir (4-28) and Amith Mishra (2-32) shared six wickets between them to put all the roadblocks they could but No.8 and No.9 batsmen Chris Morris (13 not out) and Tim Southee (7 not out) held their nerves to manage 12 required runs from the last over.
Hooda's and James Faulkner's (17) wicket in the 19th over by Tahir spelt trouble for the visitors but Mathews could not change Delhi's fortunes in the last over.
Mathews though did draw first blood at the start, sending Sanju Samson (10) back to put a brake on the Royals' run flow as Ajinkya Rahane (47) kept his cool from one end.
Mishra was introduced into the attack and the leg-spinner struck right away to get stand-in-skipper Steven Smith (11) back in the dug out with a googly.
New man Karun Nair (20) tried to take the attack to the opposition with a few boundaries but Mishra was relentless as he again struck in his second over.
The googly did it again as Nair, who had already hit two fours, tried to charge off a widish delivery only to get stumped.
The spin force continued as South African leggie Tahir trapped Stuart Binny in the 11th over of the innings.
Hooda, who hit 3 fours and 4 sixes, then joined Rahane to take the attack to the opposition after hitting Mathews for a six and two fours to help DD get 19 runs from the 13th over.
But in the very next over, Yuvraj Singh fluffed a run-out chance by spilling a good return throw by Mathews at the non-strikers end as Hooda ran to save his life.
Jaydev Unadkat created another opportunity in the 15th over, only to see Manoj Tiwary floor a catch at deep mid-wicket. Hooda again got lucky.
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