After setting a formidable target of 195, Mumbai Indians restricted Bangalore to 136 for seven in 20 overs in front of a packed crowd at the Wankhede Stadium.
Opting to bat first Mumbai Indians put up a mammoth 194 for seven in 20 overs after Dwayne Smith struck 50 and Dinesh Karthik 43.
Their bowlers put on a great show, especially local boy and medium pacer Dhawal Kulkarni (3/19), to restrict Royal Challengers to 136 for seven in 20 overs. Dwayne Smith and Harbhajan Singh also picked up two wickets each.
Smith was adjudged as Man of the Match for his all-round performance.
Kieron Pollard smashed 34 off just 16 deliveries against RCB in Mumbai.
But the credit must go to the new ball bowlers Mitchel Johnson and Lasith Malinga, who bowled an excellent line and length to tie down Chris Gayle.
Kulkarni gave Mumbai the first breakthrough as he dismissed Tilakaratne Dilshan (13) in the sixth over. Dilshan's horrid run in the season continued as his thick outside edge flew to Johnson at third man.
Much was expected from Gayle, who was coming fresh from his record unbeaten 66-ball 175 in the last game against Pune Warriors. But it wasn't the Jamaican's day. Gayle managed 18 off 20 balls before falling in the seventh over.
Harbhajan Singh (2/21) gave Mumbai the prized wicket of Gayle, who top edged and Ambati Rayudu took a superb catch at long-on. Harbhajan broke into celebrations as Mumbai had eliminated their biggest threat.
With Bangalore struggling at 37/2, Kulkarni crippled the batting as he got skipper Virat Kohli (1) and AB de Villiers (2), both caught behind by wicketkeeper Dinesh Karthik, that left the visitors at 43/4.
The battle was already lost and the lower middle-order put up some brief resistance. Saurabh Tiwary (21), Arun Karthik (12) and Syed Mohammed (9) all departed in quick successions and Royal Challengers were soon struggling at precarious 85/7.
Ravi Rampaul (23) and Vinay Kumar (26) came up with an unfinished stand of 51 that just helped them to reduce the margin of defeat.
Earlier, Dwayne Smith led the way with a stroke-filled half-century as Mumbai batting fired in unison.
With his team opting to bat, Smith blazed his way to a quickfire 36-ball 50. Karthik scored 43 off 33 balls while Pollard smashed 34 off just 16 deliveries to propel the hosts.
After being reduced to 29 for one, opener Smith stitched a 39-ball 68-run partnership with wicketkeeper-batsman Dinesh Karthik.
Smith, the aggressor of the two, continued his rich vein of form, scoring his second successive half century. The West Indian's knock comprised four fours and three sixes, before he was castled by left-arm spinner Syed Mohammad.
Mumbai suffered their first setback, when senior batsman Sachin Tendulkar, playing his first home match after his 40th birthday, was trapped leg before by R P Singh in the fourth over.
In the previous over, Tendulkar had taken a fancy to Ravi Rampaul's bowling, hitting the West Indian all over the park - over point, mid-off, mid-wicket and fine leg. Tendulkar had struck four out of his five fours in the over and scored 23 off just 13 balls.
Rohit Sharma, leading the Mumbai Indians outfit, came into bat after Smith's departure, but was run out following a mix-up with his partner.
Sharma was livid after his dismissal as Karthik, who had called for the second run, took a few paces and returned to his crease.
Mumbai, after consolidating with a 51-run partnership between Pollard and Karthik, lost wickets in a heap. The hosts lost three wickets in three balls, including those of Pollard, Karthik and a bizarre run out of Ambati Rayudu.
Pollard struck two fours and three sixes while Karthik's innings comprised of three fours and a six.