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.
Mumbai's strategy of rocking back Punjab on a track with good carry backfired because the fielders behind the wicket did not rise to the occasion.
Had Jiwanjot departed on 39 in a team score of 100 for one, if Tare had accepted a regulation catch off breakthrough man Abhishek Nayar, things could have turned out differently.
The young opener was let off two runs later, this time by Rohit Sharma off Ankit Chavan to help Punjab adjourn for lunch at 108 for one.
The Mumbai fielding was a letdown in the latter part of the day too once Jiwanjot was out to a slip catch off Kulkarni after Punjab added one run to the lunch score.
Mandeep started in aggressive fashion by pulling Chavan for two fours and a six in one over and raced to his 50 in 82 balls with the help of 8 fours and a six before luck smiled on him.
Rahane leaped in front of Hiken Shah at first slip to drop him off Agarkar on 67 and 7 runs later the same fielder grassed him off Balwinder Singh Sandhu Jr.
Ravi Inder, who often edged through the slips besides playing some authentic cuts and sweeps, departed edging Agarkar to wicket keeper Tare to bring cheers to the Mumbai camp.
But another dropped catch in the slips, this time by Rohit off Chavan, when Mandeep was seven short of his 100 proved a real dampener.
Kulkarni did find the edge of Kaul's bat after the left handed batsman added a half century stand in the last over, but Mumbai went into the dressing room at close with the knowledge that they had let Punjab off the hook due to poor catching behind the stumps.
In the morning, Mumbai lost the services of former captain and veteran opener Wasim Jaffer, who could not play in the match because of the demise of a close relative in Lucknow where he went but could not return in time.