Powered by a 38-ball 77 from West Indian Chris Gayle, who also became the first T20 batsman to score 10,000 runs, and a sublime 50-ball 64 from skipper Virat Kohli, RCB's young leg-spinner Yuzvendra Chahal sealed the deal with figures of 3/31 to restrict the hosts to 192/7 in their pursuit of 214.
Gujarat faltered once again at the start, losing the key wickets of West Indian Dwayne Smith (1) and skipper Suresh Raina (23) to Chahal.
Unperturbed by the twin strikes, former New Zealand skipper Brendon McCullum almost single-handedly raised the hopes for the hosts with a destructive 72 from just 44 deliveries.
The Kiwi right-hander first chipped in for a 36-run second wicket stand with Raina, who struck two fours and as many sixes during his 8-ball knock, and then got good support from Australian Aaron Finch (19) to raise a 66-run third wicket partnership.
Finch looked good in the middle during his 15-ball stay before being stumped off left-arm spinner Pawan Negi's slower delivery.
With Gujarat reduced to 103/3 midway through the innings, the home crowd expected an in-form Dinesh Karthik (1) to support McCullum, who at the other end raced to his half century off 30 just balls.
The Tamil Nadu stumper, however succumbed to the pressure of the mounting asking rate to be caught by Kohli off medium pacer Sreenath Aravind.
All-rounder Ravindra Jadeja then joined McCullum for a 31-run fourth wicket stand before Chahal struck once again with the wicket of the dangerous New Zealander to seal the deal in favour of the visitors.
McCullum, who by now had faced 44 balls and struck seven lusty sixes and two fours, failed to generate enough power to a slower delivery, resulting in a simple reverse-cupped catch by Adam Milne at deep midwicket.
Thereafter, young Ishan Kishan and Jadeja added 27 runs for the sixth wicket before a mix-up landed both the batsmen at the non-striker's end, ruling the local lad out for a 22-ball 23.
Needing 49 from 14, new man Andrew Tye survived a dropped chance from Kohli, who also dropped Ishan the next over.
Ishan, however provided some entertainment to the crowd with a 16-ball 39, laced with four lusty hits over the fence but that was not enough to end the home team's poor run.
Earlier, the visitors got off to a thunderous start with Gayle and skipper Kohli putting on 122 runs in 13 overs as the Gujarat bowlers failed to find an answer to the onslaught.
Kedar Jadhav (38 not out of 16 balls) and Travis Head (30 not out of 16) then finished off the proceedings in style with a 54-run unbeaten third wicket stand.
Coming into the match, just 3 runs short of becoming the first batsman to get 10,000 T20 runs, Gayle reached the landmark slicing a good length delivery from pacer Basil Thampi through point down to third man for a single.
There was no looking back from there on as the West Indian turned on the heat, dealing mostly in fours and sixes.
The 37-year-old met out special treatment to left-arm spinner Ravindra Jadeja, milking him for 21 runs in his very first over before getting to his first half century of the season off a mammoth 104-metre six from chinaman Shivil Kaushik.
Kohli, who till now was enjoying Gayle's power hitting from the other end, got down to business to get to his second half century of this year's IPL.
The 28-year-old looked good, striking seven boundaries and a six, to raise a 37-run second wicket stand with Head before pacer Dhawal Kulkarni's slower delivery did the trick for the home side.
Towards the end, Jadhav and Head showed no mercy on the bowlers, dispatching them out of the park at will as the visitors milked 35 runs from the final two overs.
Kumble-Kohli matter was not handled properly, says Sourav Ganguly
Jasprit Bumrah rises to second in T20I rankings; Virat Kohli leads batting chart
Kuldeep Yadav more lethal on dry wickets, says Virat Kohli
Ian Chappell backs Virat Kohli, says Captain can run cricket team properly
Sourav Ganguly refuses to comment on Kumble's 'untenable' remark
Sanctity of dressing room should be maintained, says Virat Kohli
Rahane will open in ODI series against West Indies: Virat Kohli
Kumble's decision to resign at last moment a personal choice, says Sourav Ganguly
BCCI tried to mediate between Kumble,Kohli says Rajeev Shukla
Gillespie blames clash of personalities for Kumble's ouster