Warner added 54 in 6.4 overs with fellow opener Shane Watson (21 off 19) and 101 in 65 balls with Steve Smith (31 off 29).
"Me and Shane had to do a job at the top there and we knew one of us had to stay there till the end, and fortunately enough tonight was my night." Warner said.
Showing remarkable dexterity, left-handed Warner hit four fours and a six from a right handed stance.
"I've been practising [switch hitting] for a fair while now in the nets," Warner said.
Australian Michael Hussey (37 off 27) got Chennai off to a rousing start before rather unluckily being adjudged lbw to a delivery from Stuart Clark (2-34 off 4), that appeared to be going over the stumps.
Spinner Stephen O'Keefe (3-28 off four) removed the other opener, Murali Vijay (17 off 16), and dismissed Suresh Raina (28 off 14), while Moises Henriques prised out M.S. Dhoni (2 off 4).
Warner effectively ended Chennai's hopes by helping to execute dismissals off successive balls in the 14th over bowled by O'Keefe, as the local team crashed to 6-112.
Bollinger (17 off 11) struck three boundaries in his highest T20 score.
Only two points separate the five teams in the group.
- AAP