Invited to bat, Gayle and skipper Kohli gave Bangalore a blistering start as they amassed 45 in the first six overs and then went on to forge a 122-run opening partnership off 76 balls at the Saurashtra Cricket Association Stadium.
Gayle's innings was studded with five boundaries and seven massive sixes, while Kohli blasted seven fours and one six in his 50-ball innings.
Kohli took the early initiative as he picked up a boundary each in the first two overs before picking Dhawal Kulkarni for a special treatment, blasting three fours of the third over.
Gayle, who has been out of form, meanwhile completed his 10,000 runs in twenty20 cricket with a single off Basil Thampi in the fourth over.
The West Indies batsman then blasted one over mid-off to score his first six of the innings. He then sent young mystery spinner Shivil Kaushik for another maximum over long-off in the seventh over.
Gayle then exploded with successive fours and a six off left-arm spinner Ravindra Jadeja. He also blasted the last delivery of the over for a maximum but he was brilliantly caught by Brendon McCullum at the long-off boundary.
But the West Indies batsman survived after replays showed that McCullum's hat had touched the boundary line.
Gayle made Lions pay as he brought up his fifty with a massive six over long on into the top-tier off Kaushik in the 10th over and then clobbered Dwayne Smith for another six as RCB reached the 100-mark.
The dashing opener sent Smith out of the park again for another six in the fourth ball over long-on as RCB picked 17 runs off the over.
In the 13th over, Basil Thampi finally dismissed Gayle when he trapped him leg before to break the partnership.
Kohli, however, continued to score runs and reached his 28th IPL fifty in the 15th over with a couple of runs off Kaushik. He then blasted a towering six over wide of long-on in the 4th ball.
Newman Travis Head (30) then sent the last ball for another maximum over deep midwicket.