Electing to bat, Chennai found scoring difficult on a pitch which had patches of grass as they failed to build partnerships while losing wickets at regular intervals at the Shaheed Veer Narayan Singh International Stadium.
Chennai, one of the most consistent IPL sides, made a slow start and lost three wickets by the halfway mark before top-scorer Faf du Plessis (29 off 23 balls) and captain Mahendra Singh Dhoni (27 off 24 balls) tried to repair the innings with a 36-run stand for the fourth wicket but in vain.
In-form opener Brendon McCullum struggled at the crease and was the first Chennai batsman to be dismissed in the sixth over bowled by Zaheer for just 11. The Kiwi drove into the hands of Delhi captain Jean-Paul Duminy at mid-off off a fuller ball outside the off-stump.
The other opener Dwayne Smith (18) and one-down Suresh Raina (11) followed McCullum to the dressing room in the ninth and 10th over respectively as Chennai suffered jolts in quick succession to be reduced to 46 for 3 at the halfway mark.
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Next over, Raina was out off a soft dismissal as he came down the track only to chip the ball straight down the throat of Duminy again off the bowling of Jayant Yadav.
Du Plessis and Dhoni tried to stitch a partnership but they separated in the 16th over. The South African dragged a Morkel delivery onto his stumps after facing 23 balls from which he hit three boundaries.
Dhoni hoisted Yuvraj Singh for a six and then got a four as Chennai took 13 runs from the 17th over. Bravo followed suit of his captain by smacking a six in the next over but perished while attempting another big hit off the bowling of Gurinder Sandhu.