The 22-year-old debutant medium pacer Lakshay Garg (2/55) rattled Bengal's top order by removing Sudip Chatterjee (1) and captain Manoj Tiwary (0) in successive overs to have them struggling at 20 for three inside 13 overs after Goa opted to bowl on an Eden Gardens green top.
But Goswami struck a 194-ball 139 (20x4) in a 213-run fifth wicket partnership with Majumdar, who remained unbeaten on 107 from 182 balls (13x4). The duo enabled Bengal seize the momentum after Goa dominated the first session.
Writtick Chatterjee was unbeaten on six along with Majumdar when bad light stopped play at 84 overs on day one.
Bengal need three points to seal a knock-out berth.
Earlier, Goa medium-pacers made full use of the conditions with Felix Alemao (1/67) giving the breakthrough in his first over of the day when he trapped Abhishek Raman (1) lbw with Bengal scorecard reading 1/1 in 1.4 overs.
Chatterjee started off slowly before Garg dismissed him.
Continuing his superb spell, Garg took the prized scalp of skipper Tiwary for a duck in his next over.
Opener Abhimanyu Easwaran (46) and Goswami steadied the boat before Goa skipper Darshan Misal brought in left-arm spinner Amulya Pandrekar.
Pandrekar cleaned up Easwaran and Bengal were reeling at 92 for four at lunch.
After the break, Goswami and Majumdar revived Bengal's innings and milked Goan bowlers with the former notching up his half-century in 86 balls. Goswami stepped up the run-rate en route to his fourth first-class century in 135 balls.
Majumdar posted his fifth first-class century off 171 balls.
Goa finally broke their double century partnership when Pandrekar dismissed Goswami.
Bengal 1st innings: 305 for 5 in 84 overs (Shreevats Goswami 139, Anustup Majumdar 107 batting; Amulya Pandrekar 2/50, Lakshay Garg 2/55) vs Goa.
Brief scores of other Group D matches:
In Amritsar: Punjab 1st innings: 395 for 2 in 90 overs (Shubham Gill 129, Anmolpreet Singh 129 batting, Gurkeerat Mann 68 batting) vs Services.
In Nagpur: Himachal Pradesh 1st innings: 287 for 6 in 90 overs (Sumeet Verma 66, Rishi Dhawan 57, Prashant Chopra 41; Rajneesh Gurbani 3/90) vs Vidarbha.
Amulya Pandrekaranmolpreet singhAnustup Majumdargurkeerat mannHimachal PradeshpunjabRajneesh Gurbaniranji trophyShreevats GoswamiShubham Gill
First Published: November 25, 2017, 6:36 PM IST