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.
Duminy blasted paceman Mohit Sharma for four boundaries in a row in the 18th over while Jadhav finished the innings with a flourish by hitting the same bowler for two sixes and a four in the final over. The two batsmen raised an unbeaten 58-run stand.
However, the DD bowlers could not complement the good work done by their batsmen.
With inarguably the strongest opening pair at it disposal, CSK expectedly made a stupendous start rattling up a 82-run stand in 11.2 overs.
Smith, continuing with his rich form, blasted three sixes off Jaydev Unadkat while McCullum too was finding boundaries although his was not the usual McCullum innings.
Of all the bowlers, used by Pietersen, it was only Wayne Parnell and Laxmi Ratan Shukla, who made an impact intially.
It was Shukla who created the first chance but Jadhav failed to hold on to a powerfully hit cut by McCullum.
However, Shukla succeeded in getting the Kiwi batsmen in his third over when McCullum could not clear the ropes at long-on.
The CSK strategy was clear. They were finding at least one boundary in each over and rotated the strike comfortably, keeping the asking rate under check.
Smith raised team's 100 with a flat six off Mohammed Shami in the 13th over and his own fifty with a four and a six off Shukla in the next.
Earlier, the DD openers took some time to settle on a seaming wicket but after getting their eye in, they cut loose.
Young paceman Ishwar Pandey bowled a rare maiden over but he was taken to task in his next by Quinton de Kock, who hit him for two sixes after Vijay struck a magnificent straight boundary.
The South African southpaw needlessly ran himself out while attempting a third run.
Skipper Kevin Pietersen failed to come out of his lean patch, scoring a golden duck. The English batsman failed to read the line of Mohit Sharma and in no time found his stumps shattered.
Despite losing two quick wickets, DD maintained a decent run rate, if not great. Dinesh Karthik creamed off a six and four off Ravindra Jadeja to take 13 runs in the ninth over and one of Murali's shots rocketed to the cover boundary as the hosts reached 75 for 2 at half-way stage.
Karthik continued the same way against pacemen as he hammered a full toss from Mohit Sharma to mid-wicket six after hitting a straight boundary off the same bowler.
He completed his fifty with a majestic cover drive. This was after he had lofted the Australian paceman with a well-calculated paddle for a six.
However, his brilliant innings was a cut short when Mohit Sharma pulled off a stunning low catch in the last ball of that over.
Vijay, from the other end, kept scoring at a brisk pace. His switch-hit off Ashwin was a treat to watch. The hosts though lost him too when he failed to connect off Jadeja while attempting a straight shot.
Two set batsmen were back in the dug out and it did affect DD's run scoring. They also lost Laxmi Ratan Shukla (0), who tried to go for an ugly hoick.
But Duminy brought respectability to the toal with his fiery knock towards the end. He blasted Mohit Sharma for four consecutive bolundaries to reel of 17 runs from the 18th over.