Chasing a small target of 124, all Chennai could manage was just 111 for six as batting was extremely tough on the M A Chidambaram wicket.
Off-break bowler Sunil Narine emerged as star performer for T&T as be bowled exceptionally well, claiming three wickets and giving away just eight runs in his four overs.
Coming into the crucial, Chennai did well in the first half by restricting the rivals to a paltry 123 for eight but the target could have been less had they not conceded 49 runs in the last five overs.
T&T managed those 49 runs largely on the back of a heroic innings from Kevon Cooper, who hit a 10-ball 28 with the help of three sixes and a four.
Opener William Perkins (34) top scored for the T and T while Adrian Barath (23) also played a useful knock.
Australian paceman Doug Bollinger (3/30) and spinner Shadab Jakati (2/18) bowled well for Chennai in the first half as they shared five wickets between them.
The target was not too big but batting was not easy and the small score proved quite difficult to achieve for the Chennai, who now have lost two of the three matches played.
Dwayne Bravo was top scorer for Chennai with his unbeaten 32 but that only reduced the defeat margin.
Now Chennai need to win their last match against New South Wales Blues on Tuesday and hope that a mathematical miracle help them make the cut for the semifinals.
T and T registered their first win and interestingly they too stand a chance to qualify for the semifinals as they take on Cape Cobras in their last group outing on Tuesday.