Half-centuries by skipper Hemang Badani, S Sriram and S Badrinath helped the visitors reach 211 for four, 59 runs behind Railways' first innings score.
Badrinath (54 not out, seven fours) played the sheet anchor's role to perfection while Sriram (59, eight fours) and Badani (54, six fours, two sixes) played attractive strokes toput Tamil Nadu in a strong position.
Hemanth Kumar was giving Badrinath company at close with nine runs to his credit.
Harvinder Singh and J P Yadav dismissed openers S Anirudha and Vidyut Sivaramakrishnan cheaply to provide a glimmer of hope to Railways.
But they were made to toil hard for the rest of the day on a pitch providing very little assistance to the bowlers.
Earlier, Harvinder played some big shots to take the Railways' score to 270 from the overnight total of 237 for eight. His 41 included three fours and a six.
Jesuraj and left-arm seamer R Naresh were the wreckers-in-chief taking four wickets each.
Badrinath and Sriram calmed the nerves in the dressing room with a 68-run stand for the third wicket which ended when the latter offered a bat-pad catch to forward short-leg offleft-arm spinner Madan Yadav.
Railways (1st innings):
Sanjay Bangar c Karthik b T Kumaran 0
Amit Pagnis c Anirudha b R Naresh 13
T P Singh c Anirudha b R Jesuraj 0
J P Yadav c Naresh b R Jesuraj 12
Raja Ali lbw b R Naresh 2
Yere Goud b R Jesuraj 71
S Khanolkar st D Karthik b R Naresh 78
S Wankhede run out 9
Harvinder Singh c Anirudha b R Jesuraj 41
K Parida c D Karthik b R Naresh 6
M Yadav not out 9.
Extras: (B-2, LB-7, W-8, NB-12) 29.
Total: (all out in 96.3 overs) 270
Fall of wickets: 1-12, 2-13, 3-21, 4-30, 5-42, 6-164, 7-193, 8-226, 9-246.
Bowling: R Jesuraj 27.3-5-80-4, T Kumaran 19-5-42-1, R Naresh 24-6-68-4, A Kapoor 13-2-34-0, S Vidyut 13-2-37-0.
Tamil Nadu (1st innings):
S Anirudha b J P Yadav 19
S Vidyut lbw b Harvinder Singh 1
S Sriram c Yere Goud b Madan Yadav 59
S Badrinath batting 54
Hemang Badani st Sanjay Wankhade b Madan Yadav 54
Hemant Kumar batting 9.
Extras: (B-8, NB-6, W-1) 15
Total: (For four wickets in 81 overs) 211.
Fall of wickets: 1-13, 2-32, 3-100, 4-188.
Bowling: Harvinder Singh 11-3-45-1, J P Yadav 17-9-20-1, Sunjay Bangar 9-2-29-0, Kulamani Parida 26-11-36-0, S Khanolkar 2-0-15-0, Madan Yadav 16-2-58-2.