Tamil Nadu face a daunting task first to score 156 more runs to avert an innings defeat and then to stop Mumbai from an outright victory.
At close, S Ramesh (31-4x4) and S Badrinath (17) were at the crease adding 28 runs for the unbroken fourth wicket.
Earlier, Mumbai were all out for 613 in their first innings, adding 100 runs to their overnight score, in reply to Tamil Nadu's 294. Mumbai's innings folded a minutes before the lunch with the hosts bowlers taking five wickets in the space of 14 overs with captain Sairaj Bahutule missing a well-deserved century by eight runs.
Bahutule was in the thick of action again, taking two crucial wickets in Tamil Nadu's second innings as the hosts yet again failed to build big partnerships on the batsmen friendly turf.
Tamil Nadu began the second innings on a positive note with captain S Suresh and Vidyuth Sivaramakrishnan (70-131b, 212m, 8x4) scoring 80 runs in 24.2 overs. However, Suresh got out giving a low return catch to Bahutule shortly before tea.
After S Sriram departed for five off the bowling of Bahutule, Sivaramakrishnan, promoted to open the batting, too made his exit, stepping out to Nilesh Kulkarni only to miss the line with wicketkeeper Vinayak Samant doing the rest.
Suresh and Sivaramakrishnan, who has opened the batting on a few occasions in the past, faced few problems, tackling new ball bowlers Avishkar Salvi (7-0-23-0) and Munaf Patel (5-0-20-0) as the hosts total reached 50 in 14.4 overs.
Wasting no time, Bahutule soon brought on experienced left-arm spinner Kulkarni in the 12th over and himself a couple of overs later.
Bahutule dismissed Suresh (36-84b, 122m, 4x4) in his sixth over with the team score on 80. Sriram, who came at the fall of the wicket, faced 29 balls for his five when he was stumped by Vinayak Samant off the bowling of Bahutule.
But, Sivaramakrishnan and Ramesh steadied the innings with the former reaching his 50 in 90 balls with the help of six fours before gifting away his wicket, by going for an unnecessary slog against Kulkarni in his second spell with just 10 overs remaining for the day.
Earlier, Mumbai overnight batsmen Bahutule (92-182b, 11x4, 2x6) and Amol Mazumdar (146-291b, 20x4, 1x6) extended their sixth wicket partnership to 181 runs, adding 50 runs in 17 overs this morning despite Tamil Nadu skipper Suresh taking the second new ball in the first over itself.
The duo got out in quick succession with the team score on 570 for seven, but, the lower order ensured the total crossed the 600 mark with wicketkeeper batsman Vinayak Samant scoring a breezy 16, which included three hits to the fence.
Left-arm spinner Sivaramakrishnan bagged three wickets for 146 runs from his 42.5 overs while R Ramkumar and C Ganapathy shared the other two wickets to fall on Monday.