Baba Indrajith top-scored with 64 for Nadu Nadu, who opted to bat after winning the toss, and Kaushik Gandhi (50) was the other half centurion for the team.
At stumps, Vijay Shankar (41) and A Aswin Crist (9) were at the crease, and the duo will look to help Tamil Nadu go past 300 on Monday at the Saurashtra Cricket Association Stadium.
Indrajith struck nine boundaries in his 114-ball knock, while Gandhi found the fence eight times and faced 137 deliveries.
Seamer Shardul Thakur and Abhishek Nayar picked up two wickets each, while there was one each for Balwinder Sandhu and Vijay Gohil.
Batting first, Tamil Nadu were off to a sedate start as openers Abhinav Mukund (38) and V Ganga Sridhar Raju (19) put on 45 runs in just under 17 overs.
It was Nayar who gave Mumbai their first breakthrough when he had Ganga Sridhar Raju, making his first-class debut, caught behind by Aditya Tare.
Skipper Mukund was dismissed when he was looking good, again caught by Tare off Sandhu's bowling, and it was then left to the duo of Gandhi and Indrajith to steady the Tamil Nadu innings.
Mumbai staged a fightback of sorts as they took four wickets after tea, including the important ones of Indrajith, who was caught down the leg side off Shardul, and Gandhi.
Vijay Shankar and Aswin Crist ensured there was no further damage with an unbroken 30-run stand late in the day, but with Mumbai having taken the new ball they will have their task cut out on the second day.