Chasing 174, Mumbai needed 16 runs off the last over, bowled by pacer Bel Hilfenhaus, and equation became 14 off the last three balls as the Australian castled Lasith Malinga off the second ball and conceded one run in the next ball.
Smith hit a towering six over long-on in the fourth ball and reeled off two conseutive fours to snatch the win for the hosts in a match, in which fortunes fluctuated like a pendulum.
Sachin Tendulkar (74) slammed his first half-century of the season and shared a 126-run stand with Rohit Sharma (60) to lay the foundation for the win but regular strikes brought Chennai back in the match.
Chennai had put up a challenging 173 for eight after being invited to bat as their top and middle-order batsmen batted superbly with Murali Vijay top-scoring with his 41.
In Image: Mumbai Indians' players celebrate their win against Chennai Super Kings