He later took three wickets for 23 in his three overs to play the leading role in his side's victory.
Chasing the big target, Chennai were on course till the 16th over as they needed 50 runs from the last four overs before the Sydney side affected two stunning catches to end their innings at 171 for nine at the New Wanderers Stadium.
Suresh Raina, who top-scored with an impressive 33-ball 57 which included eight fours and two sixes, fell in the 17th over to a stunning catch by Steven Smith who held onto a high ball just inches before the boundary ropes.
Captain Mahendra Singh Dhoni was out two balls later as his pull shot was held by Josh Hazlewood who dived forward to take a superb catch.
Chennai had two substantial partnership in their run chase -- 61 for the second wicket between Faf du Plessis (43) and Michael Hussey (16) and then the 55-run stand for the fourth wicket between Raina and Subramaniam Badrinath (6).
They began slowly in their run chase and they were dealt with a blow as Murali Vijay was out for just one in the second over as his stump flew cartwheeling while trying to hit a swinging full delivery without moving his feet.
At three for one, Chennai had to settle down for a while but they did not take much time to launch their attack with du Plessis and Hussey finding the boundaries to keep the asking rate under control.
Du Plessis punished Mitchel Starc with a six in the fourth over while Hussey also found a boundary as Chennai took 12 runs from that over.
Du Plessis then smashed three fours off Pat Cummins in the next over which yielded 13 runs before launching Hazlewood for a six and a then a four in the seventh over.