Chennai will now face Kings XI Punjab in the Qualifier 2 on Friday.
The hosts bowling failed badly in the second part of the innings as Chennai chased down the target with eight balls to spare.
Suresh Raina's performance stood out who scored an unbeaten 54. He also shared a vital 89-run stand with David Hussey (40 not out) that helped Chennai get past the target.
Dwayne Smith (24) and Faf du Plessis (35) gave a fine start with crucial contributions.
In Image: Suresh Raina bats during his match-winning innings.