Royal Challengers then rattled up 123 for three in 17.5 overs, with Gayle hitting his only six of the day to bring up the winning runs with 13 balls to spare.
With today's victory, RCB have jumped to the top of the table with five wins from their seven outings so far.
Rajasthan Royals are now in the fourth spot, with four wins from six engagements so far.
Sunrisers Hyderabad and Chennai Super Kings are in the second and third spots.
All nine teams in the tournament will play each other twice in the league before the top four advance to the play-off stage.
Gayle was the topscorer for RCB, with his 49 coming off 44 balls with the help of four fours and a six.
It was a different Gayle that the spectators saw today from the big hitting batsman they are used to seeing. He did not go after the bowlers the way he normally does, and was quite content to keep the scoreboard moving with singles and twos.
Gayle and Tilakeratne gave RCB a good start, putting on 53 for the first wicket, with the Sri Lankan doing most of the scoring and the West Indian, one of the biggest hitters in the tournament, remaining rather restrained and measured in his approach.
Dilshan left in the 7th over, caught behind by Arun Karthik off Shane Watson. Kohli, one of the highest scorers in this edition of IPL, had scored only one before he played a delivery from James Faulkner onto his stumps.
de Villiers also did not last last very long, making just 7 before Ajit Chandila took a spectacular catch at mid-off, diving to his left after the batsman smashed a delivery from Watson. At the end of nine overs, RCB were 64/3.
After that, Gayle and Saurabh Tiwary, who remained unbeaten on 25, took charge and ensured there was no further damage and slowly but surely took the home team to a convincing win. Tiwary's 25 came off 29 balls with two fours and a six.
For Rajasthan Royals, Watson took two for 11, while Faulkner got one for 21.
The visitors were largely to blame for their defeat today, given the way they collapsed from 97 for three to 117 all out in the space of five overs, losing the last seven wickets for the addition of only 20 runs.
For RCB, seamers Vinay Kumar and Rudra Pratap Singh took three wickets apiece, while Ravi Rampaul picked up two and Jayadev Unadkat and Murli Kartik one apiece. Vinay Kumar was chosen Man of the Match.
Skipper Rahul Dravid topscored for Rajasthan with 35, made off 31 balls with the help of five fours, while Stuart Binny livened up things with a quickfire 33 off 20 deliveries, studded with four fours and a six.
Opener Ajinkya Rahane (14) and Brad Hodge (13) were the only other Rajasthan batsmen to get into double figures today.
The visitors got off to a bad start, after RCB skipper Virat Kohli won the toss and put them in to bat first. They lost Watson in the third over with just 10 on the board, caught by Murali Kartik off Ravi Rampaul. At 26, Rahane left, caught by Tilakaratne Dilshan off Jayadev Unadkat.
Binny and Dravid added 40 runs for the third wicket before Binny was caught behind by Arun Karthik off Vinay Kumar in the tenth over. At the half-way mark, they were 66 for three.
Dravid and Hodge put on 31 for the fourth wicket, before the former left, caught by Rampaul off Kartik.
After that, it was a steady procession back to the pavilion, with Hodge, James Faulkner (3), Dishant Yagnik (5), S Sreesanth (0), Shaun Tait (1) and Siddharth Trivedi (3) departing one after the other. Ajit Chandila remained not out on 4.
The disciplined nature of the RCB bowling and fielding today can be gauged from the fact that they did not give away a single extra.
Shane Watson c Kartik b Rampaul 6
Ajinkya Rahane c Dilshan b Unadkat 14
Rahul Dravid c Rampaul b Kartik 35
Stuart Binny c Arun Karthik b Vinay Kumar 33
Brad Hodge c Arun Karthik b Vinay Kumar 13
Dishant Yagnik c Rampaul b Singh 5
James Faulkner c Rampaul b Singh 3
Ajit Chandila not out 4
Sreesanth lbw Vinay Kumar 0
Shaun Tait b Singh 1
Siddharth Trivedi c Singh b Rampaul 3
Total (all out in 19.4 overs) 117
Fall of wickets: 1-10 (Watson, 2.2 overs), 2-26 (Rahane, 5.2), 3-66 (Binny, 9.5), 4-97 (Dravid, 14.4), 5-105 (Hodge, 15.2), 6-108 (Faulkner, 16.3), 7-110 (Yagnik, 16.6), 8-111 (Sreesanth, 17.4), 9-112 (Tait, 18.1), 10-117 (Trivedi, 19.4)
Ravi Rampaul 3.4-1-19-2
Rudra Pratap Singh 4-0-13-3
Jaydev Unadkat 4-0-32-1
Vinay Kumar 4-0-18-3
Murali Kartik 4-0-35-1
Royal Challengers Bangalore
Tillekaratne Dilshan c Yagnik b Watson 25
Chris Gayle not out 49
Virat Kohli b Faulkner 1
AB de Villiers c Chandila b Watson 7
Saurabh Tiwary not out 25
Extras (lb 5, w 11) 16
Total (for three wickets in 17.5 overs) 123
Fall of wickets: 1-53 (Dilshan, 6.4 overs), 2-57 (Kohli, 7.4), 3-64 (de Villiers, 8.6)
Ajit Chandila 4-0-21-0
Shaun Tait 3-0-30-0
James Faulkner 4-0-21-1
Shane Watson 2-0-11-2
Siddharth Trivedi 3.5-0-26-0