The Indian outfit smashed 242-6 in Bangalore, matching the mark set by Otago Volts against Perth Scorchers in last year's competition.
Suresh Raina's 90, as well as telling contributions from Brendon McCullum and Faf du Plessis, provided the basis of CSK's huge total, before Ravindra Jadeja thumped an incredible unbeaten 40 from 14 deliveries at the end.
At one stage, Dolphins looked on course for a remarkable victory, but their innings fell away in the final stages among a flurry of wickets.
Dolphins skipper Morne van Wyk won the toss and elected to field, a decision he may have been regretting after CSK romped to 99-1 at the end of the eighth over.
McCullum then departed for 49 from 29 balls but Raina continued his assault unchecked, striking four boundaries and eight maximums in his 43-ball innings, before holing out off the bowling of Robbie Frylinck (2-52).
The demise of Du Plessis for 30 brought Jadeja to the crease and the left-hander hammered 23 from his first five balls faced, including three that cleared the ropes as CSK finished with a bang.
Perhaps inspired by Jadeja's onslaught, Cameron Delport set about the CSK bowling attack with abandon, making 34 from only nine balls, five of which went for four with two more going all the way for six.
He was eventually deceived by a clever slower ball from Mohit Sharma (4-41) which clipped the top of the stumps.
Reaching 115-3 at the halfway stage, the South African side were still in with a chance of victory, but the fall of Cody Chetty for 38 signalled the beginning of the end.
Vaughn van Jaarsveld (30) and Andile Phehlukwayo (22) did their utmost to spark a revival, but Dolphins lost wickets at regular intervals in attempting to keep up with the rising run-rate.
Mohit cleaned up Phehlukwayo from the last ball of the match as Dolphins were bowled out for 188, leaving them winless after two matches in Group A, while CSK claimed their maiden triumph of this year's event.