Tamil Nadu require another 87 runs in 90 overs with nine wickets in hand for a win on the final day tomorrow.
The home team recovered through M Vijay (not out 9, 31 balls, 1x4) and R Prasanna (not out 8, 19 balls, 1x4) after the fall of opener Dinesh Karthick (four) in the first over, to finish the day at 26 for one.
A win on tomorrow would help the team avoid relegation as it would finish their engagements with eight points as against Haryana's seven.
Earlier, the home team after being dismissed for 342 in the first innings hit back strongly to skittle out Baroda for 191 in the second essay, with off spinner R Ashwin spinning a web around the batsmen to claim six wickets.
Earlier, resuming at the overnight score of 267 for six, the home team stretched their lead to 79 runs before being all out for 342. Baroda made 263 in the first innings.
Tamil Nadu added 75 runs into the third morning in 20.3 overs after losing S Sharath (32, 71 balls, 5x4) early. He added 14 runs to his overnight score of 18, before S Vidyut (two not out) chipped in with 38 runs (64 balls, 4x4).
R Ashwin (13) and Ashish kapoor (10) also contributed to the total before the innings folded up an hour before lunch.
However, the home team, looking for the first victory of the season, came back with venom to bundle out Baroda for 191 in 55.2 overs, with off-spinner R Ashwin doing the bulk of the damage.
There were no big partnerships as Baroda lost wickets at regular intervals. Yousuf Pathan (29, 29 balls, 2x4, 2x6) and Irfan Pathan (36, 28 balls, 76x4) had starts but failed to come up with a big score. A P Bhoite, coming in at number nine, offered a brief resistance with an unbeaten 30 (41 balls, 4x4, 1x6).
Ashwin, who claimed five for 65 in the first innings, returned with a match haul of 11 for 129.
Baroda 263 and 191 (Irfan Pathan 36, Bohite 30 n o, Yousuf Pathan 29; R Ashwin 6 for 64, Ashish Kapoor 3 for 73) Vs Tamil Nadu 342 (M Vijay 121, S Badrinath 89, S Vidyut 38, S Sharath 32; Irfan Pathan 4 for 59, Yousuf Pathan 3 for 64, Bhoite 2 for 76) and 26 for 1