De Villiers smashed four sixes in his 38-ball knock, putting on 113 runs with Mandeep Singh (54no) for the third wicket to help his side recover from being only 46-2 after eight overs on Wednesday.
Dhawal Kulkarni (2-28) had bowled brilliantly for the Royals early on to dismiss Chris Gayle (27) and Virat Kohli (12), before the De Villiers show fired the hosts to a 181-run target.
Ajinkya Rahane top-scored for Rajasthan with 42, but was the only bright spot, as they collapsed to 109 all out and were knocked out of the IPL.
Having won the toss and chosen to bat first, Gayle looked to get things off to a flier and did hit one huge six and four fours in the opening overs – but he used up 26 deliveries to do so – before being bowled by Kulkarni with the final ball of the powerplay.
Kohli – starved of the strike – fell in his next over, chipping a catch back to Kulkarni when trying to turn a length ball to mid-wicket.
De Villiers and Mandeep showed little sign early on of the fireworks to come later in their innings – the latter looking particularly scratchy when taking six balls to get off the mark.
He did somewhat spoil Kulkarni’s figures, though, with a four and a six off his final two balls in the 10th over to signal the assault – Bangalore were only 60-2 at the halfway mark, before proceeding to smash 120 runs from the final 10 overs.
De Villiers brought up the fifty partnership and Bangalore’s hundred with his first six, clearing mid-wicket with the first of two slog-sweeps for maximums off Ankit Sharma in the 15th over.
Back-to-back sixes off Chris Morris in the 18th then took him to fifty, before he was run out six balls later.
Mandeep too went through to a well-deserved fifty – the first not scored by the holy trinity of Gayle, Kohli and De Villiers this year for Bangalore – as the hosts reached 180-4 from their 20 overs.
Shane Watson (10) got the Royals off to a terrific start in their reply – crunching his Australia team-mate Mitchell Starc for back-to-back boundaries in the first over, but was gone – edging Sreenath Aravind (2-20) behind – in the next.
His opening partner, Rahane, stuck around at one end but consistently lost partners at the other as their run-chase stalled.
Sanju Samson was the first to go, edging Harshal Patel (2-15) behind for five before captain Steve Smith and Karun Nair – who fell in the same fashion as Samson – both departed for 12.
Nair’s wicket was the first of six to fall for just 20 runs as Rajasthan collapsed dramatically from 79-3 after 12 overs to 99-9 in the 17th.
Rahane???s valiant effort was finally ended – caught in the deep off Yuzvendra Chahal (2-20) by that man, De Villiers – before James Faulkner was unlucky to hit the ball into his foot and offer up an easy caught-and-bowled chance for Aravind to grab.
It was the first of two wickets in two balls as Stuart Binny was then run out. Morris also fell for a duck in Starc???s next over.
David Wiese (2-32) and Chahal (2-20) then grabbed their second strikes of the innings to dismiss Hooda before the final wicket of Kulkarni ended the innings and sealed a comprehensive win.
Bangalore now fight it out with Chennai in the second IPL qualifier on Friday for a place in Sunday’s final against the Mumbai Indians.