Having bundled out Baroda for a meagre 162 in their first innings, the hosts had a real chance of registering an outright victory but their chance was jolted because of the rain-curtailed day today.
At stumps, Baba Indrajith was batting on 23 and Dinesh Karthik was also unbeaten on similar score.
Tamil Nadu, who are placed at fifth place in Group B with four draws so far, desperately need a win. The hosts still trail Baroda by 61 runs with seven wickets in hands and two days left to force the issue.
The duo put on 42 runs for the opening wicket before Karthik got out for 59-ball 23. Mukund was also quick to join his partner in the dressing room for a well-made 29.
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Baba Aparajith, who began his Ranji Trophy campaign this year with a double-ton against Services and has scored at least a half-century in every game that followed, today underestimated Yusuf Pathan's turn and was out lbw for two to leave Tamil Nadu reeling at 67 for 3.
Brief scores:
Baroda 1st innings: 162 all out in 83.5 overs (Dhiren Mistry 68; Rahil Shah 4/49, R Aushik Srinivas 3/20).
Tamil Nadu 1st innings: 101 for three in 42 overs (Abhinav Mukund 29; Yusuf Pathan 2/39).