Pollard and Rayudu targeted left-arm spinner Appanna in the eleventh over by clobbering him for 19 runs.
Pollard thrashed Appanna for two consecutive sixes, taking Mumbai to 75 for five at the end of the over.
The start of match was delayed by 50 minutes due to rain and later at about 8 pm, play was stopped again for nearly seven minutes as one of the flood lights stopped working.
Rayudu then upped the ante by clobbering a six and a four off Gayle. Rayudu got to his fifty with a cracking straight drive, keeping the Mumbai Indians in the hunt, before Pollard joined him in the onslaught.
Rayudu and Pollard provided the impetus in the 17th over, first smacking Zaheer for a six and then driving one back past the bowler for a four.
Zaheer conceded 16 runs in his third over, leaving Mumbai Indians to score 41 runs off 18 balls.
Rayudu took R Vinay Kumar to the cleaners, bludgeoning him for 16 runs, before Pollard finished the show in style.
In Image: Mumbai Indians' Keiron Pollard plays a shot