Chasing a competitive 179-run target, CSK overhauled the target with two balls to spare as the West Indies batsman led the chase with his 51-ball knock that was embellished with eight sixes and four hits to the fence.
Such was Smith's domination that he plundered boundaries at will and spared no DD bowler during his entertaining knock.
He departed in the 19th over when his side needed 11 runs off 8 balls and skipper Mahendra Singh Dhoni ensured that there was no twist in the script keeping his reputation as a fantastic finisher intact.
Dhoni hit the lacklustre Jaydev Unadkat for a six in the second ball and followed it up with a couple and a boundary through extra cover to yet again score the winning runs for his side.
Brendon McCullum (32) and Suresh Raina (47 not out off 26) too contributed in CSK's win, supporting the rampaging West Indian well.
Light shower made it a pleasant evening for the fans but for Daredevils it continues to be gloomy affair as it became difficult to grip the wet ball.
With this win, CSK have strengthened their position at the top while Delhi will now find it extremely difficult to go beyond the first stage of the tournament.
It was one of the better wickets seen at Kotla, making it possible to have a good contest between ball and bat.
Initially it helped pacers while gradually stroke-making became easier.
Despite losing charismatic skipper Kevin Pietersen for a golden duck, Daredevils put up a competitive 178 for five, thanks to a collective batting effort, led by Dinesh Karthik
Karthik smashed his way to a 51-run knock and combined well with Murali Vijay (35) for a splendid 71-run partnership for the third wicket after a shaky start.
JP Duminy (28) and Kedar Jadhav (29) provided superb finishing touches with their fiery cameos as DD put on board their best total of the season after being invited to bat.