Brendon McCullum scored 32 off 35 balls before being dismissed by Laxmi Ratan Shukla.
Suresh Raina scored an unbeaten 47 off 27 balls.
Wayne Parnell celebrates with his team-mates after dismissing Dwayne Smith for 79 runs.
Chasing Delhi's 179, Dwayne Smith (79) and Suresh Raina (47*) put up a partnership of 86 runs to guide Chennai to a eight-wicket win with two balls to spare.
Dinesh Karthik led a collective batting effort with a fighting 51 as Delhi Daredevils scored a competitive 178 for five against Chennai Super Kings.
JP Duminy (28 not out) helped Delhi put on their best total of the season on board after being put into bat at Feroz Shah Kotla.
Mohit Sharma exults after dismissing Delhi captain Kevin Pietersen for a duck.