David Warner (68) top-scored in Australia's innings, with Matthew Wade (56) and David Hussey (54) also scoring half-centuries.
Hussey's knock featured the game's biggest talking point after he was given not out for handling the ball when on 17, a decision that angered Indian skipper MS Dhoni.
The Victorian used his right hand to block a throw from Suresh Raina prompting the Indians to appeal but the umpires decided Hussey's actions were an attempt to avoid injury, rather than shield the stumps.
India's innings began badly with Virender Sehwag (5) brilliantly caught and bowled by Ben Hilfenhaus (2-50) before Warner ran out Sachin Tendulkar (14) in what was most likely be the great batsman's final innings at the SCG.
When Watson came on and removed Virat Kohli (21) and Raina (8) in quick succession, the visitors' resistance had crumbled.
Irfan Pathan smashed two big sixes in his entertaining 22 but Xavier Doherty (2-26) and Brett Lee (1-26) wrapped up the tail to complete the victory with 10 overs to spare.
Dhoni was unequivocal about Hussey's handled ball situation.
"Plain and simple that was out,'' he said after the match.
"In this case I think David was really lucky, I think he should have been given out but it's not in my hands that he was not given out.
"It's difficult, in his judgment he may have been protecting himself but his hand was too far out.''
Dhoni also said he felt Tendulkar's run-out shouldn't have been given because he had been impeded by Lee but neither decision affected the final outcome.
Watson said he was comfortable umpires Billy Bowden and Simon Taufel had made the right calls on both occasions.
"Simon Taufel and Billy Bowden are two of the best umpires in the world so I've got total trust always in their decisions,'' he said.
"Dave Hussey would never do anything untoward. He plays the game hard but fair.''
Watson said he felt fine physically and was ready to lead again if Clarke is unable to return to the lineup for Friday's game at the MCG.
- AAP
