Replying to Kerala's first innings score of 165 all out, the hosts were in some spot of bother at 67 for three before Muzumdar and Bhavin Thakkar (34 off 108 balls) first steadied the rocking boat with a 75-run fourth wicket stand off 30 overs.
Muzumdar and left-hander Kambli then consolidated their team's position with 114-run stand off 24.3 overs in 113 minutes.
First to go on Wednesday morning was Wasim Jaffer (21 off 82 balls) who fished out side the off stump only to be caught by wicketkeeper C M Deepak off Prashant Chandran, who went on to finish with five for 53.
Night watchman and skipper Sairaj Bahutule was the next to go when he was caught by Hemanth Kumar at mid-off off Chandran for 29 off 100 balls.
Then Thakkar and Muzumdar came good before the former was caught and bowled by Chandran and then Muzumdar was run out for 85 that came in 251 minutes with eight fours.
Ramesh Powar hung in for some time before being caught by Sony Cheruvathore at mid-on off Chandran for 21 and then Robin Morris became Chandran's fifth victim when his edge was snapped up by skipper Sunil Oasis for no score before the umpires called off play for the day due to bad light with still three overs to be bowled.
Mumbai rips through Kerala