"Game plan was really simple for us. Try to bowl straight lines, back of a length and it worked out."
Cummins was back in the team after being benched for four matches.
"Last few games on the bench, been a good time to look at our bowlers. Tim Southee has bowled fantastically well. So yeah just when I get a chance to try and be a little more disciplined."
Five-time champions Mumbai, who were winless for eight matches this season before getting two wins, have already bowed out of final-four contention.
Venkatesh, a left-hand batsman, gave Kolkata a brisk start as they reached 64-1 in the first six overs after being put into bat first.
Venkatesh smashed four sixes in his 24-ball knock but fell short of his fifty after being caught at covers in his attempt to go big again.
Rana took on the opposition bowlers in a 26-ball blitz and Kolkata looked like getting past 190 before Bumrah came roaring back in his second over.
Bumrah, who had picked up just five wickets in the previous 10 matches, struck twice and followed that with a triple-wicket maiden in his third over.
He sent back the big-hitting West Indian big-hitter Andre Russell for nine and had Rana caught behind.
He took three wickets in four balls but Tim Southee averted a hat-trick.
Rinku Singh hit an unbeaten 23 and denied Bumrah a sixth wicket in the 20th over, playing out five dot balls before taking a single on the final delivery.
"When you contribute with wickets it's always a good feeling, but the very important thing is to make the team win," said Bumrah who was named man of the match.
"We got into a good position but midway through the innings the pressure creeped on and we lost the game."
In reply, Mumbai lost Rohit Sharma for two, caught behind off Southee as Kolkata successfully reviewed the call in their favour after the on-field umpire denied the appeal.
Russell struck twice with his pace bowling, but Ishan Kishan attempted to revive the chase in his 43-ball 51.
Mystery spinner Varun Chakravarthy took down Tim David for 13 and Cummins struck three times including Kishan and Daniel Sams in one over to turn the tide in Kolkata's favour.
Kolkata wrapped up the Mumbai innings in 17.3 overs with three run outs including Kieron Pollard for 15.