Watson, 34, struck six sixes in his 124 not out off 71 balls as the hosts made 197-5, but India chased the total down by hitting 19 off the last over.
Suresh Raina (49) struck a four off the final ball when needing two to win.
He was ably supported by Rohit Sharma (52) and Vihat Kohli (50) as India won by seven wickets in Sydney.
Named captain in place of the injured Aaron Finch, Watson looked to have put the match beyond the tourists with his first T20 hundred after he won the toss.
He surpassed the previous second highest T20 score of 123, made by New Zealand's Brendon McCullum against Bangladesh in 2012.
The highest individual score is the 156 by Finch against England at Southampton in 2013.
Shane Watson hit the second highest Twenty20 international score but India still whitewashed his Australia side in the three-match series.