Chasing 164, Bangalore completed their third victory in 19.3 overs after Gayle and de Villiers hit half-centuries.
Gayle made 87 off 56 balls with four sixes and eight fours while de Villiers scored 52 from 39 balls with six boundaries.
Their partnership was the fourth century stand and the highest for any wicket so far in the tournament.
For Punjab, medium-pacer Parvinder Awana captured four wickets for 34 runs.
Earlier, Bangalore captain Daniel Vettori won the toss and put Punjab into bat who scored 163 for six in the allotted 20 overs.
Main scorers were Australiann batsman David Hussey hit 41 and Pakistan-born English county allrounder Azhar Mahmood, who was playing his first match in the tournament, remained not out on 33.
Seamers Zaheer Khan and Andrew McDonald claimed two wickets each for Bangalore.
Pakistan’s first sports tv channel Geo Super televised this match live from Mohali
