Yuvraj (52 not out) shared 84 runs from just 7.9 overs with captain Virat Kohli (49 not out) for the unconquered third wicket as RCB chased down the target of 146 with 20 balls to spare at the Sharjah Cricket Stadium.
Yuvraj, who received criticism from some quarters for his slow batting in India's loss against Sri Lanka in the recent World T20 in Bangladesh, began tentatively but came to his own later as he hit three fours and five sixes in his 29-ball unbeaten knock.
Kohli, who was adjudged player of the tournament in the World Twenty20 for top-scoring with 319 runs, continued with his top form in T20 though he was dropped twice -- on 23 and 24. He hit two fours and three sixes in his 38-ball unconquered innings.
The duo competed in hitting fours and sixes towards the end of their run chase after opener Parthiv Patel had done well at the top of the innings with a 28-ball 37 which was studded with five fours and a six.
RCB left out Chris Gayle due to a back problem but made a strong start though they lost IPL debutant Nic Maddinson (4), the young opener from Australia, in the second over. The other opener Patel and one-down and captain Kohli eased off the pressure of the early jolt with some sensible batting. The duo's 50-run partnership came at the eighth over from just 5.5 overs with Patel finding more boundaries than his captain. Patel hit five fours and a six while Kohli could get just one boundary in the 50-run stand.
Patel perished while trying to play shots, too many than required, with leg-spinner Rahul Sharma cleaning him up as RCB were reduced to 62 for two in the ninth over. Next-man in, Yuvraj looked tentative in the beginning but hit some lusty blows to ease off pressure.
Kohli was let off on 23 and 24 in the space of five balls in the 13th over, the unfortunate bowler being Wayne Parnell, by IPL debutant Jimmy Neesham and Mayank Agarwal respectively.
Kohli and Yuvraj responded with a six each off Neesham to shrug off the let off by taking 15 runs in the 14th over. The Kohli-Yuvraj duo then decided to end the contest quickly as the duo took 20 runs from 15th over bowled by Rahul Sharma.
Kohli smashed two sixes while Yuvraj hit a maximum to add to the misery of Rahul who bled 33 runs from his three overs though he took a wicket.
Earlier, the Daredevils found themselves in tatters before Jean-Paul Duminy's brilliant unbeaten half century took them to a decent 145 for four.
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.
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 and two maximums off Ashok Dinda.
Coming together at 35 for four, the pair added 96 runs in the second 10 overs after the Daredevils could score just 49 for four at the halfway mark due to the initial jolts. The last five wickets yielded 63 runs with Duminy and Taylor scoring 14, 13 and 17 from the final three overs.
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.
RCB captain Kohli opted to bowl after winning the tossand straightaway put the Daredevils in tatters by scalpingtheir top three batsmen in the space of just eight ballsbetween third and fifth overs.
Opener Mayank Aggarwal (6), captain Dinesh Karthik (0)and Manoj Tiwari (1) made brief appearances at the creasebefore they fell to Starc, Morkel and Aaron respectively asthe Daredevils were reduced to 17 for three in the fifth over.
The other opener Murali Vijay (18) was though shaping upwell as he smashed a huge six off Starc and then a four offMorkel before he also perished without contributing much.
Young Haryana leg-spinner Chahal, debuting for RCB inIPL, bowled him with a beauty as the ball straightened afterpitching to knock down Vijay's off-stump as the Daredevilsfound themselves in dire straits at 35 for 4.
The responsibility of taking Daredevils to a respectabletotal was left to Taylor and Duminy and the duo grafted for runs before opening up later on to take Daredevils score to145 for four.