After restricting RCB at 148 runs for the loss of four wickets, Punjab reached 150 runs by losing only two wickets.
Hashim Amla (58*) and Australian Glenn Maxwell (43*) added 72 runs in the third wicket partnership to reach the winning scorecard.
Maxwell thrashed three boundaries and four sixes in his knock.
Amla hit four boundaries and three sixes in the match.
Earlier, it was star South African batsman AB de Villiers and his heroic 46-ball 89 runs unbeaten knock that helped the side score 148 runs on the scorecard.
AB hammered nine sixes and three fours in the knock.