Chasing a daunting 191 to win, Rajasthan were staring down the barrel after losing five wickets for 106 runs in 14th over but Smith (48 off 21) and Faulkner (41 off 17) combined well to find boundary after boundary.
In complete mayhem, the Australian duo scored the last 65 runs off just 17 balls to not only secure the win with seven balls to spare but also steal the thunder from Yuvraj Singh, who had roared back to form with a strokeful; 83 and followed it up with four wickets.
It all started in the 17th over as Faulkner creamed off two fours and a six off the fellow Australian Mitchel Starc. Smith began the next over, bowled by Ashoke Dinda, with a six and two shots to the fence.
Faulkner then finished it off quickly in the 19th over, punishing Varun Aaron with two sixes and a four, stunning the RCB camp and the home fans.
With this win, Rajasthan have strengthened their position in top-four although they remained in third position with 10 points. RCB are still at sixth place with six points.
Bangalore owed their big total to Yuvraj and AB de Villiers (58) as they shared a magnificent 132 run stand, which powered RCB to 190 for five after electing to bat.
Yuvraj, who was dropped on 47 by Sanju Samson, and de Villiers put up a gallant fight as RCB scored 84 runs in the last five overs to snatch the momentum from their rivals, who were well in command till 12 overs.
Sending the Rajasthan bowlers on a leather-hunt, the hosts belted 120 runs in the last eight overs.
Rajasthan too had to endure a bad start as Yuvraj rocked the visitors middle-order with his spin, starting the rot with the important wicket of skipper Shane Watson (1).
The left-armer also scalped Rajasthan's top scorer Karun Nair (56), Stuart Binny (1) and very talented Sanju Samson (13) to end with figures of 4-0-35-4.
Rajasthan were reeling at 106 for five in the 14th over but what followed was complete mayhem. From nowhere, Smith in company of James Faulkner changed the game with their amazing ability to bat under pressure.
Steven Smith played a blinder, scoring 48 off 21 balls with four sixes and as many fours while Faulkner hit three sixes and three fours in his 17-ball knock.
Yuvraj, who received criticism for his slow batting and failures in this IPL, punished the bowlers with seven fours and seven sixes in 38-ball knock.
De Villiers, who is the most consistent batsman of RCB, continued with his splendid form in T20, punished the bowlers with five sixes and a four.
Yuvraj and de Villiers were competing in hitting fours and sixes towards the end of the innings after RCB had a disastrous start, losing three wickets for 40 runs in 8.1 overs.
RCB innings was off to a disastrous start after their captain Virat Kohli, who opened the innings instead of Parthiv Patel, returned to the dugout cheaply in third over.
Kohli tried to smash the ball over extra-cover, got a thick edge that went into the hands of Rajat Bhatia stationed at third man off Kane Richardson.
The mighty West Indian Chris Gayle, who is yet to get a big score under his belt in this IPL, started his innings sedately but shifted gears by smashing two boundaries in Pravin Tambe's first over for nine runs.
However, in the next over the oldest IPL player had the last laugh by having Gayle reaching for a googly and was caught by Sanju Samson behind the stumps after he had made 19 off 25 balls with three boundaries.
Vijay Zol, who played his first match of the season, made 16 runs off 14 balls with three boundaries, before he thick edged right-arm legbreak Rahul Tewatia's wrong one to captain Shane Watson standing in first slip.