The 25-year-old Sharma, who is yet to fulfill his dream of becoming a Test cricketer after having played the first of his 85 ODIs five years ago, struck 19 fours and three sixes in his 243-ball innings. Mumbai were 364 for three in 109 overs at the close of play.
Giving company to Sharma, who compiled his 14th first class ton, was in-form batsman Hiken Shah, who was not out on a watchful 54 off 163 balls with five fours.
The home team was 216 runs behind Punjab's 580 with plenty of batting to come.
The fourth-wicket duo, who came together at the fall of Kaustubh Pawar - dismissed by Harbhajan Singh - have so far added 171 runs for the unbroken fourth wicket in 329 balls, Sharma's contribution being 108.
The second and third wicket partnerships also fetched Mumbai 74 and 87 runs respectively.
Mumbai, 69 for the loss of Aditya Tare's wicket yesterday, added 295 runs while losing Ajinkya Rahane and Pawar (78 in 176 balls with 9 fours), during the day.
For Punjab, Harbhajan, Manpreet Gony and Sidharth Kaul shared the three wickets.
With Sharma and Shah -- who came into the game with three back-to-back Ranji hundreds against his name -- going strong and Abhishek Nayar - the second-best run getter for the team behind Shah this season - skipper Ajit Agarkar and Ankit Chavan to follow, Punjab have their task cut out.
Brief scores: Punjab 580. Mumbai 364 for 3 in 109 overs (Kaustubh Pawar 78, Rohit Sharma 163 batting, Hiken Shah 54 batting; Manpreet Gony 1-68, Sidharth Kaul 1-55, Harbhajan Singh 1-71).
