Brendon McCullum's 33-ball 47 helped Kochi chase down a revised victory target of 135 in the rain-hit game, which was reduced to 17 overs a side.
Earlier, Suresh Raina scored a brisk half-century to help Chennai to 131 for four, a total which eventually proved insufficient against the new IPL entrants.
Batting first after losing the toss, Murali Vijay gave Chennai a solid start scoring 28 off just 18 before being trapped lbw by Thisara Perera.
Raina and Subramaniam Badrinath then took the team to 68 for two in nine overs, when a heavy downpour interrupted play.
Raina and Mahendra Singh Dhoni seized the initiative once the play resumed after a 90-minute break with the experienced campaigners scoring at a healthy rate.
Raina, who added 48 off six overs with Badrinath (18), brought up the visitors' 100 with a six and soon reached his half-century off 39 balls, but the left-hander ran himself out in the very next ball.
Dhoni (14) and Albie Morkel (nine) hit two sixes off the last over of the innings, but Kochi did well to restrict Chennai to 131 for seven.
Chasing a revised target, using the Duckworth-Lewis system, of 135 for victory, Kochi were cruising until Mahela Jayawardene (16) was dismissed by Ravichandran Ashwin, who had conceded a six and a boundary in the previous two balls.
Parthiv Patel joined McCullum at 39 for one after 4.3 overs and the duo kept Kochi in the hunt taking the team to 66 at the first interval.
McCullum then moved up a gear, hitting back-to-back fours off Tim Southee, but Ashwin soon had the dangerous opener, who holed out in the deep three runs short of a half-century.
With 45 required off 39, Brad Hodge joined Patel and the pair kept the home side on course adding 20 in quick time, but Doug Bollinger dismissed the left-hander for a 26-ball 34.
However, Hodge (19 not out) and Ravindra Jadeja (16 not out) unleashed a flurry of big shots to finish things off with a couple of overs remaining.