Warner made an undefeated 63 in 41 balls after rain had interrupted play in the first over of the Australian innings.
India captain Mahendra Singh Dhoni was unable to stem the flow of runs despite using eight bowlers including part-timers Yuvraj Singh, Virat Kohli and Rohit Sharma.
Earlier, Dhoni won the toss and chose to bat first but his team were restricted to 140 for seven. Opener Irfan Pathan top-scored with 31.
Australia pace bowler Pat Cummins brilliantly ran-out opener Gautam Gambhir for 17 by kicking the ball on to the stumps.
The in-form Kohli also fell for 15 before Watson removed Yuvraj (eight) and Pathan in the same over.
Cummins finished with figures of two for 16 in four overs.
INDIA innings
G. Gambhir run-out 17
I. Pathan c White b Watson 31
V. Kohli c Christian b Cummins 15
Y. Singh c Maxwell b Watson 8
R. Sharma b Starc 1
S. Raina c Maxwell b Watson 26
MS Dhoni c Bailey b Cummins 15
R. Ashwin not out 16
H. Singh not out 1
Extras: (b-2, lb-2, w-6) 10
Total: (for seven wickets, 20 overs) 140
Fall of wickets: 1-21, 2-56, 3-70, 4-74, 5-74, 7-137.
Bowling: Maxwell 2-0-11-0, Starc 4-0-27-1, Cummins 4-0-16-2, Watson 4-0-34-3, Christian 2-0-19-0, Hogg 4-0-29-0 (w-2).
AUSTRALIA innings
S. Watson v sub. (Tiwary) b Y. Singh 72
D. Warner not out 63
G. Maxwell not out 4
Extras: (w-2) 2
Total: (for one wicket, 14.5 overs) 141
Fall of wickets: 1-133
Bowling: Ashwin 3.5-0-32-0 (w-1), Zaheer Khan 3-0-18-0 (w-1), Harbhajan Singh 2-0-20-0, Chawla 1-0-14-0, Pathan 1-0-19-0, Kholi 1-0-10-0, Yuvraj Singh 2-0-16-1, Sharma 1-0-12-0.