Mandeep made a strokeful 211.
Replying to their rivals' huge score, the home team was 69 for the loss of opener Aditya Tare's wicket, with Kaustubh Pawar (26) and Ajinkya Rahane (18) at the crease.
The 39-time champions have a formidable task to try and make 512 runs more to take the first-innings lead.
The morning belonged to Mandeep and Amitoze who put the Mumbai attack to the sword by rattling up 163 runs in just 31.2 overs, with Amitoze being the aggressor.
Mandeep, not out 102 overnight, played second fiddle to his partner who was batting on 83 off 109 balls with 11 fours and 2 sixes in a team score of 451 for four at lunch. Mandeep was 169 not out at the break.
Amitoze left soon after lunch for 91, after facing 115 balls in 163 minutes, and his knock contained 11 fours and three sixes.
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Mandeep, dropped thrice before he reached his ton yesterday, was let off again on 199 today. In all he cracked 32 fours and a six. His previous highest score was 193.
The 20-year-old Jalandhar-born batsman put on 195 in just 217 balls for the fifth wicket with Amitoze.
Amitoze was the first to go after lunch and then Punjab lost three more wickets quickly, including Mandeep, who offered a no shot to be bowled by spinner Ankit Chavan.
But the tail wagged with the last two wickets adding 66 runs to pile on the agony for Mumbai.
Mumbai lost Tare to Manpreet Gony in reply, trying to flick the ball off hips and offering a tame return catch.
Brief scores: Punjab 580 (Jeevanjot Singh 42, Ravi Inder Singh 76, Mandeep Singh 211, Amitoze Singh 91; A Agarkar 3 for 95, Dhawal Kulkarni 2 for 106, Ankit Chavan 3 for 142). Mumbai 69 for 1.