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.
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.
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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.
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.
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.