After restricting Bangalore to a modest 135 for eight by claiming two quick wickets, the Queenslander hit his second successive half century, both match winning knock, to help Rajasthan earn their third successive win in four matches.
Bangalore crashed to their second defeat and now has just one win in three matches.
Watson added 104 for the third wicket with South African skipper Graeme Smith 49 (42b, 8x4) to give no chance for the home team to make something out of its modest score.
He had hit a match-winning half century over Deccan Chargers just two days ago. Today the Aussie was again at his fluent best. He played without taking risk in the beginning and then opened out in style. He hit 26 runs off a Praveen Kumar over, hitting five boundaries and a huge six in the 14th over of the innings to take the visitors to a comfortable victory.
Chasing a modest 136 to win, by and large a small total in view of even 200 is now achievable in this league as shown by Royals themselves against the Laxman"s men, Royals made a negative start losing Mahesh Rawat in the first over and then lost big hitter Yusuf Pathan (21) early with Praveen Kumar and Zaheer Kahan striking in tandem.
However their success did not last long as the Australia-South African pair took the match away from Rahul Dravid"s men.
Earlier, the Royals bowlers struck to a good line and made maximum use of the bouncy track to restrict Bangalore to 135 for eight, with Watson and Munaf Patel claiming two wickets apiece.
Royals skipper Shane Warne marshalled his bowlers very well as his batsmen gave him no hick ups what so ever in achieving the winning target.