Vignesh was joined by Natarajan when the score was 310 for 9 with Tamil Nadu needing another 28 runs to surpass Bengal's tally of 337.
Vignesh struck 30 off 38 balls with three fours and a six while Natarajan defended doggedly for his 10 runs as Tamil Nadu finished the day at 348 for 9.
At the start of the day, Abhinav Mukund (45) and Kaushik Gandhi (65) added 100 runs for the second wicket before Agniv Pan's direct throw found Mukund short of his ground.
Dinesh Karthik top-scored for Tamil Nadu with a valuable 80 off 117 balls with 11 boundaries. He added 58 runs Baba Indrajith (34).
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However both the Baba brothers were out in quick succession to Sayan Ghosh (4/121) who was getting the old ball to reverse.
Once Karthik edged one from Amit Kuila to Goswami behind the stumps at the score of 281, there was a fair chance for Bengal to take first innings lead but the Tamil Nadu tail wagged vigorously with Aswin Crist hitting a quickfire 36 with the help of two fours and two sixes.
Bengal captain Manoj Tiwary did not use Pragyan Ojha (2/48 in 14 overs) much. Neither did he use off-spinner Aamir Gani, who went for 19 runs in his 7 overs that he bowled.
Brief Scores: Bengal 1st Innings 337
Tamil Nadu 1st Innings 348/9 (Dinesh Karthik 80, Kaushik Gandhi 65, Abhinav Mukund 45, K Vignesh 30, Sayan Ghosh 4/121, Pragyan Ojha 2/48).