Chasing 159 to win, the Royals got the required runs in the final over of the match and never looked in trouble against a toothless RCB side.
Buttler and skipper Ajinkya Rahane made a strong start to the innings, taking the home side to 55/0 after the end of the powerplay.
However, Rahane would depart shortly after the field restrictions were lifted, failing to read a googly from Yuzvendra Chahal that trapped him plumb in front of the stumps.
Undeterred, Buttler continued his assault alongside Smith, who played the sheet anchor role as the explosive Englishman kept the scoreboard ticking.
Even after Buttler departed after holing out to Marcus Stoinis after failing to connect with a slow leg-spinner from Chahal, the home side remained firm favourites to emerge on the winning side.
A 50-run partnership between Smith and Tripathi – aided by numerous dropped chances – all but snuffed out whatever slim chances of victory RCB had, despite the fact that Smith got out at the fag-end of the innings.
Tripathi and Ben Stokes easily got the remaining runs in the final over of the match, the former finishing the match with a massive six over deep mid-wicket.
Earlier, Shreyas Gopal starred with the ball for RR, taking 3-12 – his second-best figures in IPL history – as RCB could only score 158/4 after being put in to bat.
Gopal got the prized scalps of Virat Kohli and AB de Villiers before accounting for the dangerous Shimron Hetmyer as well.
Kohli promoted himself up the order, coming out to open the innings alongside Parthiv Patel. However, it was the latter who would go on to have more of an impact on the match.
The RCB and India skipper played it steady to begin with but was absolutely foxed by a googly from Gopal which went on to castle his stumps, much to the delight of the leggie.
His next over saw him get rid of De Villiers with another wrong one. AB failed to read the ball and gently played it back to Gopal, who completed a good forward diving catch to complete the dismissal.
He then accounted for Hetmyer in his penultimate over, getting the batsman to poke at a ball that offered a relatively straightforward catch to Buttler behind the stumps.
Parthiv – who had kept the scoreboard ticking with some attacking strokeplay despite the loss of wickets – was able to eventually bring up his half-century off 29 balls.
Stoinis looked to up the ante at the other end, but despite getting away the odd boundary he struggled on a surface that offered assistance to slower bowlers.
Parthiv’s departure in the 18th over only added to the pressure on the Australian all-rounder yet it was a cameo from Moeen Ali that played a key part in RCB ending the innings strong.
He scored 18 runs off 9 balls – including a six and a four in the final over – before Stoinis played a cheeky scoop to end the innings with another boundary.