Resuming at their overnight score of 250 for three, the hosts were bowled out for 467 runs off 136.4 overs in 585 minutes half an hour before tea.
Left-hander Nishit Shetty (54 off 111 balls) and Muzumdar added 132 runs off 19.1 overs for the fourth wicket to put their team in a solid position.
Muzumdar, who was batting on 56 when the stumps were drawn yesterday, occupied the crease for 279 minutes to score his 131 runs which also included 13 fours and one six while Shetty, who resumed his batting on 26, was at the wicket for 141 minutes for his 54 hitting five fours and a six.
Also contributing to Mumbai's huge total were Ramesh Powar (29) and Vinayak Samant (34) while Gujarat medium pacers Lalit Patel (two for 73), Ashraf Makda (two for 98) and spinners Timil Patel (three for 115) and Kirat Damani (two for 65) were among the wickets for the visitors.
Gujarat took the second new ball after 100 overs with the score reading 324 for three and left-arm seamer Makda struck immediately having Shetty caught behind the wicket by Nilesh Modi.
The other medium pacer Lalit Patel then struck two quick blows accounting for Mumbai skipper Sairaj Bahutule (17) and then plotting the down fall of the centurion.