South African great De Villiers made it three unbeaten half centuries for the tournament, lofting Jofra Archer over deep midwicket for his sixth maximum to make it 55 off 22 deliveries and seal the points with two balls to spare.
Rajasthan set Bangalore 177-6, as Steve Smith returned to form with an excellent 57 from 36 deliveries, but they have now lost four of their past five matches.
The Royal Challengers are third with six wins from nine outings and their other standout performer was Chris Morris, whose 4-24 include the scalps of Smith, Jos Buttler and Ben Stokes.
Bangalore lost Aaron Finch for 14 after a couple of sixes early in the run chase as the Australia opener sliced a slog sweep off Shreyas Gopal high into the air.
Skipper Virat Kohli (43) and Devdutt Padikkal combined in an assured stand of 79 for the second wicket but departed in consecutive balls when trying to force the pace, leaving their side 102-3 in the 14th over.
Enter De Villiers, who took the attack back to Rajasthan with able support from Gurkeerat Singh (19 not out). He made his move decisively at the start of the penultimate over, when he bludgeoned Jaydev Unadkat for three consecutive sixes.
Earlier, a reshuffled Rajasthan order paid dividends for their captain Smith, who dropped down to four after a succession of single-figure scores.
Robin Uthappa’s breezy 41 accounted for the bulk of a half-century opening stand with Stokes (15) but they were 69-3 when Sanju Samson fell to Yuzvendra Chahal.
Smith rebuilt alongside Buttler (25) and remained until the final over, when Morris added the Australia star and Archer to his haul. It might have been enough, but for the inimitable De Villiers.
De Villiers turns in another masterclass
“I’m very, very nervous and erratic [in a run chase] and I get very stressed like any player,” De Villiers said when being presented with the man-of-the-match award. Spare a thought for Unadkat, in that case. The left-armer might feel he was hung out to dry by Smith handing him the 19th over. His first delivery was crashed over midwicket, with a slower ball dispatched beyond wide long-on next ball.
A dismissive swipe over square leg followed before a single from an attempted yorker ended the assault. De Villiers and Gurkeerat still needed 11 from Archer’s final over, but the momentum had unquestionably shifted.
Buttler loses out in Rajasthan reshuffle
While a move down the order worked for Smith, the same could not be said for England big-hitter Buttler. Demoted from opening alongside Stokes, he scored an unusually circumspect 24 off 25 deliveries before holing out to Morris.
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