De Villiers hit 19 fours and four sixes in his innings, putting on an IPL-record partnership of 215 with Virat Kohli (82 off 50 balls) as RCB posted a massive 236-run target from their 20 overs.
Lendl Simmons smashed an unbeaten 68 from 53 deliveries and Kieron Pollard hit a 24-ball 49 as Mumbai made a good fist of the run chase, but still fell some way short on 196-7.
In a crucial game, with both occupying spots outside of the play-off places before play, Bangalore won the toss and chose to have first use of the Wankhede stadium batting track.
Chris Gayle (13) started ominously with a six off Mitchell McClenaghan in the first over, but was then dropped ??? as was Kohli ??? in the New Zealander???s next over.
Rohit Sharma???s drop of Gayle wasn???t too costly as he fell to a stunning catch from Simmons at short third man off Lasith Malinga in the next over.
But Harbhajan Singh???s drop of Kohli did come back to haunt them as the RCB captain built a record partnership with the new batsman, De Villiers.
The pair pushed Bangalore up to 88-1 after 10 overs before launching an incredible onslaught, with 147 runs coming from the final 10 overs and 88 from the final five.
De Villiers brought up his second IPL ton in the 17th over with one of four big sixes in his knock.
Kohli played a more understated knock at the other end but tonked two fours and a six from the final over to fire Bangalore to 235-1.
Parthiv Patel (19) was the first wicket to fall in Mumbai???s reply, run out by that man Kohli.
Their captain, Rohit Sharma, was the next to go, falling to Harshal Patel (2-36). But Simmons and Pollard then put on 70 together in 6.1 overs to keep them in the contest.
Pollard fell one short of fifty, holing out to a great catch from Mitchell Starc in the deep off Sreenath Aravind, reducing the hosts to 133-3 in the 15th over.
That dented the momentum of the Mumbai innings and wickets continued to tumbled, with only Ambati Rayudu (14) and McClenaghan (12) ??? who smashed a pair of sixes apiece ??? passing double figures.
The 39-run win for Bangalore sees them into fourth in the IPL table, while Mumbai???s play-off push is fading in sixth.