Put into bat, the Daredevils were reduced to 35 for four in the eighth over with their top order batsmen coming a cropper before Duminy (67 not out) and Ross Taylor (43 not out) shared 110-runs for the unbroken fifth wicket stand at the Sharjah Cricket Stadium.
The duo built the innings by grafting for runs initially before opening up towards the end. Duminy especially slogged at the death overs as he hit a six off Yuvraj Singh and two maximums off Ashok Dinda.
Duminy, the more aggressive of the duo, hit four boundaries and three sixes in his 48-ball unbeaten knock while Taylor smashed four boundaries in his 39-ball unconquered innings.
For RCB, Mitchell Starc, Albie Morkel, Varun Aaron and Yuzvendra Chahal took a wicket each.
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RCB captain Virat Kohli opted to bowl after winning the toss and straightaway put the Daredevils in tatters by scalping their top three batsmen in the space of just eight balls between third and fifth overs.
The other opener Murali Vijay (18) was though shaping up well as he smashed a huge six off Starc and then a four off Morkel before he also perished without contributing much.
Young Haryana leg-spinner Chahal, debuting for RCB in IPL, bowled him with a beauty as the ball straightened after pitching to knock down Vijay's off-stump as the Daredevils found themselves in dire straits at 35 for 4.