Opting to field, Chennai restricted Yorkshire to 140 for six on the back of impressive bowling from pacers Albie Morkel (2/12) and Doug Bollinger (2/16)and then romped home with six balls to spare in the inconsequential Group B match at Kingsmead.
S Badrinath top-scored with a 38-ball 47 which he made with the help of four boundaries while Mahendra Singh Dhoni, who played under Suresh Raina's captaincy in the match, made 31 from 23 balls. Raina himself contributed 31 from 30 balls.
Chennai, the 2010 champions, ended third in Group B with eight points behind Sydney Sixers and Highveld Lions, the two teams who made it to the semifinals.
Wriddhiman Saha, who kept wickets in the match as Dhoni also decided not to wear the wicketkeeper's gloves, hit the winning run -- a single -- as Chennai reached 141 for six in the last ball of the 19th over.
Chasing 141 for a win, Chennai did not have the best of starts as they lost opener Faf du Plessis (1) in the second over of the bowling of Steven Patterson.
The other opener Murali Vijay (13) struck two fours in the next over before he was out in the fifth over. Vijay wanted to hit Hannon-Dalby to midwicket fence but the ball did not take the full face of the bat as it went up high to land into the hands of Adam Lyth at square-leg.
Chennai were then at a wobbly 26 for two but Raina and Badrinath settled down quickly and shared a 48-run stand for the third wicket from 6.9 overs to take Chennai closer to the target.