Nair (64 off 45) and Rishabh Pant (36 off 22) set the platform for Delhi before regular fall of wickets pushed them back a bit.
Delhi, going against the trend, chose to bat after picking a side comprising eight Indians and three foreigners, becoming the second team to do so this season after Gujarat Lions.
Captain Zaheer Khan said at the toss that his players were "looking to express themselves" after already being out of the play-off race.
Nair and Pant then got together and took the attack to the opposition. No boundaries were scored in the first three overs but they made up for that by smashing five fours and six in the next three. Both batsmen looked in cracking form.
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Similar treatment was meted out to Pune's star all- rounder Stokes, who went for 13 in his opening over, courtesy three crisp hits from Nair.
Pant was not be kept quiet at the other end and his standout shot was the massive six over mid-wicket that almost landed on the dressing room balcony. Trying for another big one, Pant departed the next ball after being caught at long on off Adam Zampa, leaving Delhi at 83 for three in nine overs.
Just when Delhi seemed set for a big score, Dhoni swung the momentum in Pune's favour with some outstanding glove work. Showing he was still one of the best in the business, Dhoni sent back Samuels with a one-hand catch on the jump before dismantling the stumps in a jiffy to remove Corey Anderson.
Nair had gone quiet while wickets well at the other end. He got to first half century of the IPL with a single.