Both the teams seek return to winning ways after losing their respective previous games.
But Pollard's 26-ball unbeaten 46 helped the three-time champions post 136/7.
Alzarri Joseph's dream debut, which saw him register the best bowling figures in IPL history, helped Mumbai defend a modest total of 136.
The young Windies pacer ended with sensational figures of six for 12 in 3.4 overs.
Alzarri Joseph broke Sohail Tanvir’s record of the best bowling figures in the IPL (6/14) set in the inaugural edition of the IPL in 2008
Mumbai Indians trumped the hosts Sunrisers Hyderabad at the Rajiv Gandhi International Stadium, Hyderabad with a 40-run win in Match 19 of the IPL 2019 on Saturday.
Joseph has featured in nine Tests and 16 ODIs for the West Indies so far.
Mumbai are believed to rope in West Indies fast bowler Alzarri Joseph as a replacement.
The West Indian Test and ODI skipper also stated that he wants to be the best all-rounder in all formats.