Kallis (58 not out) carried his bat through the innings, hitting two boundaries and two sixes from 56 balls, to steer Bangalore to their seventh win from 13 matches.
Kallis first shared a 70-run stand from 69 balls for the second wicket with Rahul Dravid (34-ball 38) and then combined with Ross Taylor (12-ball 25) for 29 runs from just 14 balls for the third wicket to take Bangalore home with one over to spare.