The 20-year-old Jalandhar-born batsman, who went into the game with just 89 runs from five matches this season, utilised fully the three chances offered by the butter-fingered Mumbai fielders to remain unbeaten on 102 at the Wankhede Stadium.
Mandeep, who pulled and drove handsomely while striking 14 fours and a six off left-arm spinner Ankit Chavan, was dropped on 67, 74 and 93 in the slips before reaching his maiden first-class hundred in his 22nd game with an on-driven four in 162 balls.
He had batted for 228 minutes and faced 168 balls.
Mandeep put on a stand of 128 in 204 balls for the third wicket with Ravi Inder Singh, who made 76 with the help of 14 fours.
Mandeep then added 51 runs for the fourth wicket with another left-hander, Uday Kaul (19) to further cement Punjab's position before the latter fell to the last ball, edging a rising ball from Dhawal Kulkarni to the slip cordon.
Ravi Inder also added 52 runs for the second wicket with in-form opener Jiwanjot Singh who came into the match with 619 runs in his debut season with two hundreds and a double hundred. The latter got two 'lives' in his 42 off 121 balls.
Punjab, put into bat by Mumbai skipper Ajit Agarkar, started well on a track assisting seamers with Jiwanjot, who hit six fours, and Karan Goel (25) laying a good platform by adding 57 runs.
The latter departed after edging Agarkar to Ajinkya Rahane who later let off Mandeep twice in the second slip.
Jiwanjot was then let off twice in close succession by wicket-keeper Aditya Tare and Rohit Sharma, but he could not take full advantage of the lives.
Brief scores: Punjab 288 for 4 (Jiwanjot Singh 42, Ravi Inder Singh 76, Mandeep Singh not out 102; Ajit Agarkar (2 for 54), Dhawal Kulkarni (2 for 61) versus Mumbai.