Chasing 195 runs to win the match, RCB lost their skipper and Chaser-in-chief Virat Kohli for a mere 14 runs.
Though Lokesh Rahul and Ab de Villiers played a brisk innings each, it proved inadequate as their innings progressed no further than 179 runs.
Continuing his form, Rahul scored yet another half-century, the second in a row and the same in his IPL career. His 28-ball innings of 51 runs was compiled with six boundaries and a six.
AB fell three short another fifty, hitting two sixes and three fours.
Watson, who earlier picked up a wicket, and was one of the most economical for his side, could manage only two runs as he was run out.
Sachin Baby tried to up the ante, hitting a couple boundaries but was stopped by an experienced Nehra.
Kedar Jadhav remained unbeaten at 25 off 15 balls.
Earlier, asked to bat first, Sunrisers skipper David Warner went hammer and tongs as the Aussie sent the RCB bowlers for a leather hunt during his 50-ball knock of 92 runs.
Though Warner missed out on a century, he was able to take the Orange Cap from his RCB counterpart.
Losing their first wicket for a modest 28 runs in form of Shikhar Dhawan (11), Kane Williamson and Warner forged a 124-run partnership for the second wicket.
Williamson too scored a fine fifty off 37 balls and struck seven fours.
Among the RCB bowlers, Kane Richardson picked up two wickets, with Watson and Shamshi picking up one each.
Warner was elected the Player of the match.
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