Chennai, the 2010 and 2011 champions, chose to bat first and made 177-7 in their 20 overs with Suresh Raina making 56.
Delhi were skittled out for 84 in their reply as they slumped to their second loss in three matches.
Dwayne Smith made 29 for Chennai at the top of an order as they reached 50-1 at the end of the powerplay despite the loss of Brendon McCullum for nine.
Raina hit five boundaries and a six in his 41-ball innnings and was supported by Faf du Plessis, who made 24 from 17 balls, and Indian captain Mahendra Dhoni who blasted 32 from just 15 balls.
Despite an impressive 3-32 from young seamer Jaydev Unadkat, the Daredevils—still missing injured captain Kevin Pietersen—faced a tough chase at nearly nine runs per over.
|Chennai Super Kings: 177-7 (20 Overs)|
|Dwayne Smith||b Shahbaz Nadeem||29||28||103.57||3||0|
|Brendon McCullum||c sub (Wayne Parnell) b Jaidev Unadkat||9||10||90.00||1||0|
|Suresh Raina||c Murali Vijay b Jimmy Neesham||56||41||136.58||5||1|
|Francois du Plessis||c Murali Vijay b Mohammed Shami||24||17||141.17||1||1|
|MS Dhoni||c Mayank Agarwal b Jaidev Unadkat||32||15||213.33||2||2|
|Ravindra Jadeja||c Dinesh Karthik b Jaidev Unadkat||7||3||233.33||0||1|
|Mithun Manhas||NOT OUT||13||5||260.00||2||0|
|Ravichandran Ashwin||run out (Mohammed Shami)||1||1||100.00||0||0|
|Ben Hilfenhaus||NOT OUT||0||0||0.00||0||0|
|EXTRAS||(w 3, lb 3)||6|
That task was made far tougher as they slumped to 50-5.
After losing three men in the opening 26 balls, they were further hit with the loss of key men JP Duminy and Ross Taylor.
The South African was trapped lbw by Smith for 15 at the start of the ninth over, and the New Zealand batsman fell in the next over for six, caught behind off Ben Hilfenhaus.
The team, who are much revamped after losing 13 of their 16 games last season, folded inside 16 overs as Ravi Jadega and Ravichandran Ashwin shared the final four wickets with Nathan Coulter-Nile unable to bat.
|Delhi Daredevils: 84 (15.4 Overs)|
|Mayank Agarwal||c Suresh Raina b Ishwar Pandey||2||7||28.57||0||0|
|Murali Vijay||c Francois du Plessis b Mohit Sharma||11||12||91.66||2||0|
|Dinesh Karthik||b Ravichandran Ashwin||21||22||95.45||2||0|
|Manoj Tiwary||c Francois du Plessis b Ishwar Pandey||0||2||0.00||0||0|
|JP Duminy||lbw Dwayne Smith||15||14||107.14||0||0|
|Ross Taylor||c MS Dhoni b Ben Hilfenhaus||6||6||100.00||1||0|
|Jimmy Neesham||c Suresh Raina b Ravindra Jadeja||22||15||146.66||2||0|
|Shahbaz Nadeem||c Suresh Raina b Ravindra Jadeja||3||8||37.50||0||0|
|Mohammed Shami||c Brendon McCullum b Ravichandran Ashwin||1||3||33.33||0||0|
|Jaidev Unadkat||NOT OUT||1||5||20.00||0||0|
|Nathan Coulter-Nile||Absent hurt||0||0||0.00||0||0|
|EXTRAS||(w 2)||2||EXTRAS||(w 2)||2|