Put into bat, opener Dwayne Smith (34) and middle-order batsman Faf du Plessis (32) provided a good platform for Chennai but Delhi's spin trio of Amit Mishra (1/21), Imran Tahir (1/27) and J P Duminy (1/15) bowled beautifully to restrict Chennai to a modest score.
With wickets tumbling, Mahendra Singh Dhoni too found the going tough. In the end, the Chennai skipper blasted two sixes in the last over to take his team close to the 150-mark.
Australian pacer Nathan Coulter-Nile was the highest wicket-taker for Delhi as he scalped three for 30 in his four overs at the MA Chidambaram Stadium.
Earlier, Smith gave Chennai a flying start as he blasted three fours in the opening over to amass 16 runs.
His opening partner Brendon McCullum (4) too smashed a boundary in the first ball of the next over but Nathan came back strongly, dismissing the New Zealand captain in the next ball to strike an early blow.
Nathan struck again in his second over as he cleaned up Suresh Raina to reduce Chennai to 38 for two.
New man du Plessis then joined Smith and blasted a couple of boundaries off Domnic Joseph and Albie Morkel.
Delhi skipper Duminy introduced spinners Imran and Amit next and the plan worked as the South African gave a simple catch to Nathan at deep midwicket while looking for a boundary.
Next batsman Ravindra Jadeja didn't waste any time as he cracked a four and six within 10 balls of his stay, while du Plessis indulged in singles and twos to keep the scoreboard ticking with spinners bowling in tendum.
After 12 over, du Plessis hit Duminy for a four over extra cover but he was dismissed in the next ball when he tried to smash another ball for a boundary, only to be caught by Shreyas Iyer at the fence.
India skipper Mahendra Singh Dhoni then joined Jadeja but the latter could not stay longer as he was foxed by Mishra's googly which sent his stumps for a walk.
Domnic Joseph then joined the party, getting rid of Dwayne Bravo with a delivery that trapped him in front of the wicket as Chennai slipped to 120 for six in 16.4 over.
Dhoni tried his hand and blasted two sixes in the last over before holing out to Mayank Agarwal as Chennai posted 150 in the end.