Defending a low total of 138 runs, Punjab dismissed the star-studded RCB batting line-up for 119 runs in 19 overs.
Medium-pacer Sandeep Sharma and left-arm spinner Axar Patel were the stars of the show with three wickets each.
Patel returned figures of 3/11 in four overs while Sandeep took 3/22.
The win keeps Punjab in the running for a spot in the play-offs as they have 10 points from an equal number of matches, while RCB have been knocked out of the reckoning as they have a mere five points from 12 matches.
Except for opener Mandeep Singh who made 46 runs off 40 balls before bowled by Glenn Maxwell, none of the RCB batsmen could tackle the Punjab bowlers.
The dominance of the Punjab bowlers can be gauged from the fact that only three RCB batsmen could reach double figures.
Earlier, RCB restricted Kings XI Punjab to 138/7 in their allotted 20 overs.
Patel (38 not out) and Manan Vohra (25) were the major contributors to Punjab's cause.
Punjab got off to a poor start as openers Hashim Amla (1) and Martin Guptill (9) were sent back to the pavilion inside five overs.
Amla was dismissed by medium pacer Aniket Choudhary on the penultimate ball of the first over and Guptill was dismissed by Sreenath Aravind in the fourth over.
With 18/2 in 3.3 overs, Marsh and Vohra tried to stabilise the innings and they were almost successful but after adding 21 runs in 3.3 overs the latter was sent packing by spinner Pawan Negi. In his 17-ball knock Marsh slammed three boundaries.
Vohra, who seemed good at the middle was also dismissed by Yuzvendra Chahal in the 12th over. Vohra's 28-ball knock was laced with one boundary and one six.
Skipper Glen Maxwell (6) also failed to rise to the occasion as he was also dismissed by Chahal in the very next over.
Middle-order batsmen Wriddhiman Shah (21)and Patel then forged a 34-run partnership to help the visitors to get past the 100-run mark.
But soon, Shah, who played 25 balls and slammed one boundary, was bowled by Shane Watson in the 18th over.
In the very next over, new batsman Mohit Sharma (6) was also dismissed with the scoreboard reading 119/7.
The last over saw some boundaries from Patel but that was not enough for Punjab to post a challenging total.
For Bangalore, Choudhary and Chahal scalped two wickets each while Aravind Watson and Negi chipped in with one wicket each.