After the undefeated 122-run fourth-wicket stand between de Villiers (59 off 23) and Tillakaratne Dilshan (76 off 58) propelled Bangalore to 189 for three, Appanna bemused the Rajasthan batsman with his slow left-arm bowling, which saw him return figures of 4/19, at the Sawai Mansingh Stadium.
Appanna weaved his magic after De Villiers consumed just 21 balls to get to his fifty. While Dilshan hit 10 fours and a six, de Villiers smashed three fours and five sixes during their partnership, which came off just 50 balls.
Chasing a stiff target, Rajasthan were off to a flying start, with skipper Rahul Dravid (58 off 42) leading the way by racing to his fifty in just 34 balls. Rajasthan crossed the 50-run mark in good time but the in-form Ajinkya Rahane`s dismissal to Appanna came as a setback.
23-year-old left-arm spinner, Appanna was drafted into the playing XI for this match in place of Arun Karthik.
Dravid, during his stay at the crease, played some innovative shots all round the wicket but, faced with the daunting task of keeping pace with the ever-increasing required rate, the senior pro needed more from his team-mates.
Even as Dravid reached his half-century with a four through cover, Appanna defeated Owais Shah in flight after the batsman came down the wicket only to be stumped by de Villiers for 10.
The former India skipper lofted Appanna through the deep midwicket region, but Dravid was again letdown as Sreevats Goswami, promoted ahead of Brad Hodge, miscued a shot to give a simple catch to the deep midwicket fielder.
Finally, it was Dravid himself who succumbed to the pressure, spooning a turning Appanna delivery to extra cover. After Dravid and Hodge departed, it was just a matter of time for the Royal Challengers to emerge victorious.
The positive result brought Bangalore level with the other top teams with four wins. Earlier, Bangalore were in a spot of bother at 67 for three in the 12th over after being invited to bat by Dravid.
To start with, Bangalore`s plans were a bit spoiled after an unwell Chris Gayle could not open the innings. The opening combo of Virat Kohli and Dilshan failed to give Bangalore the start they were looking for, as the former was dismissed by pacer Pankaj Singh with just 23 on the board in the fourth over.
Mayank Agarwal got a start but could not consolidate, with Brad Hogg having him caught by another Australian Brad Hodge at the deep.
Hogg dealt Bangalore their biggest blow of the innings when he trapped danger man Gayle for a cheap score, to leave the visitors struggling at 67 for three in the 12th over. But the momentum seemed to have swung Bangalore`s way after de Villiers joined Dilshan at the crease.
De Villiers was on the money straightaway, hitting Ajit Chandila for two successive sixes -- the first over deep midwicket, for the first of the innings, and then charged down the wicket to slam the bowler over the same region.
The fifty stand was up in just 23 balls as Dilshan picked Siddharth Trivedi for a six and four in the 16th over. De Villiers then hit Kevon Cooper and Trivedi for three more sixes, two off the later, to help Bangalore finish the innings on a high.