Kallis took the wind out of Otago’s sails by reducing them single-handedly to 32 for three as they chased a daunting target.
Unable to recover, the New Zealanders were dismissed for 108 in the 18th over, with only five batsmen reaching double-figures – captain Craig Cumming being the top-scorer with 20.
Kallis finished with 3/18 off four, while the crafty Anil Kumble bagged two wickets.
Earlier, Kallis struck a superb 59-ball 73 – including four boundaries and two sixes – to lead Bangalore to a very competitive 188 for two.
Kallis and Robin Uthappa gave the hosts the best possible start as they raked up a first wicket stand of 75 before the latter was caught off Aaron Redmond for 42.
Virat Kohli played a little gem of an innings as he punished all the bowlers in a double-quick 32-run cameo.
Ross Taylor produced a flurry of runs at the end of the innings, scoring 32 off only 11 deliveries.
Teams:
Royal Challengers Bangalore: RV Uthappa, JH Kallis, R Dravid, V Kohli, LRPL Taylor, MV Boucher (wk), B Akhil, RE van der Merwe, R Vinay Kumar, P Kumar, A Kumble (capt) Otago Volts: BB McCullum, AJ Redmond, HD Rutherford, CD Cumming (capt), NT Broom, NL McCullum, AD Mascarenhas, IG Butler, DC de Boorder (wk), WC McSkimming, N Wagner