At stumps, Tamil Nadu were 60 for 1 having lost opener MS Washington Sundar (4), bowled by Ashoke Dinda.
Bengal started the day at 190 for 3 and left-hander Agniv Pan (59) was bowled by Thangarasu Natarajan with the second new ball in the fifth over of the day.
Chetterjee, who had hobbled out yesterday on a personal score of 34 after suffering from a pulled hamstring, walked in at Agniv's departure.
Goswami hit six boundaries before an angle delivery from Krishnamoorthy Vignesh saw him edge one to Narayan Jagadeesan behind the stumps.
Also Read
Chatterjee continued calmly hitting the occasional boundaries and also taking the singles. He hit nine boundaries in all as he reached his 7th first-class hundred in 249 deliveries.
He found a valuable partner in Ashok Dinda (21), with whom he added 42 runs as the duo took the score past 300 runs. Pragyan Ojha (14) also contributed a bit with the bat which all added to the final score.
He had surpassed half-century mark in all of Bengal's previous three games with scores of 73 (vs UP), 51 (vs Punjab) and 85 (vs Railways) but the three-mark was eluding him this season.
Having been in the 'A' team radar for some time, Chatterjee played a timely knock.
For Tamil Nadu, Vignesh was the most successful bowler with 4/70 in 32 overs while left-arm spinner R Aushik Srinivas had 3/67 in 36 overs.
When Tamil Nadu batted, skipper Abhinav Mukund was caution personified as he scored only 19 off 74 balls which had four boundaries. Mukund played a lot of dot balls -- 67 in all as he was more intent on either dead batting or leaving deliveries outside the off-stump.
Brief Scores: Bengal 1st Innings 337 (Sudip Chatterjee 100, Agniv Pan 59, Manoj Tiwary 56, Krishnamoorthy Vignesh 4/70).
Tamil Nadu 1st Innings: 60/1 (Abhinav Mukund 19 batting, Kaushik Gandhi 25 batting, Ashok Dinda 1/21).
Disclaimer: No Business Standard Journalist was involved in creation of this content