Chasing a mammoth 192 to win, the home team managed just 134 for nine in their stipulated 20 overs, in what was essentially an insipid batting display.
It was the Mumbai team's 10th win in 13 matches in this edition, third on the trot after successive losses, and further consolidated their place at the top of the table with 20 points.
It also helped them square their head-to-head record against the team from Bangalore to three wins apiece, one each in this edition.
As regards the Royal Challengers, they finished their league campaign with seven wins and seven defaets to end up with 14 points.
Royal Challengers, who had won six of their seven matches batting second, came up short on this occasion with the result affecting their net run-rate to a considerable extent.
The loss also jeopardised their semi-final prospects - RCB can still qualify for the semi-finals but might end up facing Mumbai Indians away from home. A win at home would have helped them avoid MI in the last four.
Virat Kohli [ Images ] was the lone Bangalore batsman to put up a semblance of a fight. His 24-ball 37 comprised four hits to the fence and one over it.
Kieron Pollard was the pick of the Mumbai bowlers with figures of three for 28.
In the next over Jacques Kallis [ Images ] (14) was cleaned up by Ryan McClaren, leaving the home team tottering at 34 for two at the end of the Power Plays - worse than the MI total at the same stage.
But the off-spinner had Rahul Dravid [ Images ] (16) caught by Kieron Pollard at short midwicket in his second over to have the hosts tottering at 58 for three going into the first strategic timeout (after nine overs).
Pietersen smashed a Harbhajan delievery over midwicket for a maximum but the bowler hit back three balls later, with the South Africa-born Englishman failing to read a doosra and hitting straight to Saurabh Tiwary [ Images ] at long-off.
Ross Taylor [ Images ] (9) didn't last long either, hitting a Fernando delivery straight to Harbhajan at deep midwicket. A perfect yorker from Zaheer dislodged Dale Steyn's [ Images ] (0) stumps in the next over.
And when Kohli perished to Pollard in the penultimate over, it was all over.
Earlier, Mumbai Indians made a tepid start, cut loose in the middle before eventually finishing strong.
The visitors made 191 for four in their stipulated 20 overs.
MI, the table toppers, had managed just 75 in their first 10 overs, but smashed a mammoth 116 runs in the last 10.
JP Duminy [ Images ] ensured his side finished on a high note, scoring an unbeaten 19-ball 42, a knock that was inclusive of three hits to the fence and three over it.
Ambati Rayudu began the resurgence with a superlative 47 in the middle of the innings.
Mumbai Indians surprised somewhat by promoting Ryan McLaren [ Images ] (40) up the order to open with his captain. The move didn't have the desired impact though as the batsman struggled to break free.
Dale Steyn bowled a tight first over but Sachin Tendulkar [ Images ] (19) tried to cut loose in the second over (off R Vinay Kumar) hitting successive boundaries, the first flicked towards the leg side and the second forced through the cover point.
However, the Bangalore bowlers, to their credit, bowled a tight line in the Power Play period not allowing the Mumbai batsmen to break free.
And they were backed in their endeavour by some great commitment shown by their fielders.
The frustration of not being able to play his shots and the pressure to accelerate the scoring rate got the better of Tendulkar and he hit a Jacques Kallis delivery straight to Ross Taylor at deep square leg - it was Kallis' 10th wicket in this edition.
As the field restrictions eased (after six overs), the team from Mumbai had managed just 34 and lost the vital wicket of Tendulkar - without doubt the slowest start in the tournament for the table toppers.
In the seventh over, McLaren hit a Pankaj Singh delivery straight to Rahul Dravid at short midwicket but the latter surprisingly spurned the opportunity.
MI reached the 50-run mark only in the ninth over, Ambati Rayudu (46) ensuring it with a boundary towards backward square-leg.
He celebrated the same with successive sixes over long-on, the second of the shot being a chance dropped and parried over by Vinay Kumar.
The ninth over - by Singh - cost Bangalore a whopping 22 runs, and MI batsmen returned to their dug out - for the first strategic timeout - having boosted their confidence to an extent.
Rayudu continued his onslaught, hitting successive sixes off Kumble, both smashed over long-on.
McLaren tried to clear the fence as well but hit straight to Steyn, only for the latter to put it down.
It was Kumble's second over and it cost him 16 runs, besides the missed opportunity.
Rayudu smashed successive boundaries off Kallis before the latter had the last laugh, catching the batsman off his own bowling.
Rayudu's 27-ball 46, inclusive of three boundaries and four maximum, was nonetheless the kind of innings MI desperately needed to give their total the required fillip.
The second-wicket stand between Rayudu and McClaren yielded MI 69 runs off just 31 balls, with the former palpably doing most of the damage.
Going into the second strategic timeout, taken after the 13th over, MI had come back well to be placed at 103 for two.
Soon after resumption, McClaren finally managed to cut loose, hitting Kumble for a couple of boundaries, the first past the bowler and the second, a quick glance towards fine leg.
And Kieron Pollard (20) got into the act in the next over (off Singh) hitting three successive sixes - the bowler conceding 22 runs in that over for disappointing overall figures that read thus: 4-0-54-0.
However, Kumble brought Bangalore right back into the game by trapping the West Indies [ Images ] all-rounder plumb in front with a quicker one.
The introduction of Kevin Pietersen into the attack in the 17th over yielded RCB a wicket first ball, the Englishman catching McClaren plumb in front.
JP Duminy carried forward the momentum though, smashing 19 runs of the 18th over by Kallis, including two maximums.
The South African hit a paddle scoop to secure the lone boundary off Steyn's bowling in the day - the fast bowler's impressive figures read 4-0-18-0.
A dozen came of the last over, with both Duminy and Abhishek Nayar (9 not out) helping themselves to a boundary each.
The duo put on 49 runs, off just 23 balls, in an unbroken fifth wicket stand.
Earlier, Royal Challengers Bangalore captain Anil Kumble [ Images ] won the toss and invited Mumbai Indians to bat.
"It's a good surface to bat though it might be on the slower side. We will try to restrict them and then chase it down," reasoned Kumble, adding, "We would like to qualify for the semi-finals on points."
His opposite number, Sachin Tendulkar, wasn't too perturbed.
"The pitch has got a bit of grass but looks good to bat on," he said.
The start was delayed following a few low intensity blasts outside Gate No.12.
Royal Challengers: Anil Kumble (captain), Jacques Kallis, Manish Pandey, Kevin Pietersen, Robin Uthappa, Virat Kohli, Ross Taylor, Rahul Dravid, Dale Steyn, R Vinay Kumar, Pankaj Singh.
Mumbai Indians: Sachin Tendulkar (Captain), Aditya Tare, Ambati Rayudu, Saurabh Tiwary, JP Duminy, Kieron Pollard, Abhishek Nayar, Harbhajan Singh, Zaheer Khan, Dilhara Fernando, Ryan McLaren.