Mumbai Indians restricted Chennai Super Kings to just 114/9 in their ten-wicket win.
Boult (4/18) and Bumrah (2/18) did major damage, and along with leg-spinner Rahul Chahar (2/22) and fellow quick Nathan Coulter-Nile (1/25), restricted CSK to just 114/9, which also they could reach only because of all-rounder Sam Curran's (52) fighting half-century.
Pollard, who led the defending champions on the night due to an injury to regular skipper Rohit Sharma, was pleased with the bowling performance.
"It's part and parcel of it, sometimes you don't actually have to be a leader, I know a thing or two. So it was just a matter of me stepping in and it came off tonight," he said at the post-match presentation, as quoted by ANI.
"It was just a matter of making the right decisions, not giving them freebies. We wanted to bowl them out under 100 but Sam batted well. I think it was a total team effort. Two-three wickets early puts you in the game and to get 4-5 is fantastic," Pollard added.
In the second half, carrying on from where the bowlers left, MI openers Quinton de Kock (46*) and Ishan Kishan (68*) dominated the proceedings. The magnificent duo made short work of the task and helped MI clinch a ten-wicket win with nearly 8 overs to spare.
"And then the openers going out and finishing off and not leaving any uncertainty was good. We want to finish top two and it's a matter of getting the points and then think about the opponents," Pollard said.
"There's always room for improvement, myself making some mistakes on the field, guys not being aware in certain situations. Maybe it's no technical, but it's things you need to speak about," he added.
The emphatic victory took MI to the top of the points table with seven wins in ten outings. The team next face Rajasthan Royals (RR) in Abu Dhabi on Sunday (October 25).