Watson, who also took three for 34 with his seam bowling, won his third straight man of the match award in the tournament after lashing seven sixes and two fours in a 42-ball 72 as his side reached their target of 141 with 31 deliveries to spare.
Warner made an undefeated 63 in 41 balls after rain had interrupted play in the first over of the Australian innings.
"The last couple of games have been pretty good," Watson said. "It's nice when things come together like this."
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.
"Once the ball got wet it was very difficult for our spinners," said Dhoni. "There was no real grip for them.
"That was one of the main reasons we were not able to put pressure on the Australian batting line-up."
Dhoni defended the decision to leave out hard-hitting opener Virender Sehwag for the second successive match.
"We choose our 11 depending on the opposition that we are playing and also what kind of wicket we are playing on," he said.