While Bangalore are now placed third in the table with 15 points, the Warriors slumped to their seventh straight defeat to continue to languish at number eight.
Gayle (57 off 31) and Dilshan (53 off 44) helped Royal Challengers to a challenging 173 for three after they were asked to bat by new Pune skipper Steven Smith.
Regular Pune skipper Sourav Ganguly 'rested' himself in the match and the side made as many as five changes but nothing helped them as they swallowed yet another defeat.
Chasing 174, the hosts made the worst possible start as paceman Zaheer Khan removed Mohnish Mishra (4) and Manish Pandey (0) in the very first over.
Australian skipper Michael Clarke (13) yet again came a cropper as all Pune managed was 138 for nine in 20 overs.
R Vinay Kumar (3/32), Muttiah Muralitharan (2/16) and Zaheer (2/21) all contributed in Pune's rout by striking intermittently.
Robin Uthappa's fiery 38 before being stumped off Muralitharan and Anustup Majumdar's sensible knock of 31 was the only resistance that came from the home side.
Earlier, Gayle and Dilshan laid a very strong platform for a big score and later Saurabh Tiwary (36 not out off 30) also contributed in team's total.
The visitors had a fiery start, yet again thanks to Gayle's pyrotechnics with the bat. Gayle and Dilshan put on 80 runs for the first wicket in just 51 balls.
Gayle was his usual attacking self as he smashed six sixes, four in one over of Bhuvaneshwar Kumar, to score the fastest fifty of the season in just 24 balls.
Dilshan played second fiddle to Gayle but later on took the responsibility to guide the side to a decent total.
Sri Lankan paceman Angelo Mathews was the most economical and successful bowler for Pune as he gave away just 14 runs in his three overs also dismissed destructive Gayle.
