Coming in to bat when Mumbai were tottering at 101 for four after lunch, Yadav (120) and Vinit Indulkar (82), playing his first match for Mumbai after returning to its fold following a three-season stint with Himachal Pradesh, hit back in style to help the hosts steady the boat.
Maharashtra bounced back late in the day when medium pacer Anupam Sanklecha dismissed both the batsmen, while Samad Fallah took the wicket of Shardul Thakur (4).
The visitors had the 40-time champions on the rack after winning the toss, but they let the game slip away when Yadav, who batted for 209 minutes and faced 139 balls while hitting 18 fours, attacked the bowling. Indulkar also chipped in with important runs as he played the supporting role to a nicety.
23-year-old Yadav compiled his first ton in 15 matches and after a gap of over two years, his last coming in December 2011.
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He hit 17 fours in 115 balls when he reached the milestone, his fourth first class century and third in the championship for Mumbai.
Sanklecha got rid of the obdurate Indulkar late in the day when he edged behind after a stay of 252 minutes in which he struck 13 fours off 164 balls. He then struck another blow with the second new ball by packing off Yadav through a catch to second slip.
At the other end, Fallah grabbed the wicket of Thakur to see that Maharashtra ended the day on a happier note.
Medium pacers Fallah and Sanklecha grabbed three wickets each, while first change Shrikant Mundhe took the other wicket to fall. Spinners Akshay Darekar and Chirag Khurana were unlucky not to pick up one apiece after chances were missed by their captain and wicketkeeper Rohit Motwani off their bowling.