Virat Kohli equalled Ricky Pontings record of 41 international centuries as captain to place India on the brink of an innings victory.
The tourists finished the next day of the next Test at Kolkata trailing by 89 runs with four wickets in the next innings remaining.
Kohli put India in control with 136.
Ishant Sharma promised 4-39 to lose Bangladesh from the first Exam that was day-night to 152-6 to be held in India.
The hosts, who lead the two-match series 1-0, look set to seal wins with just two weeks to spare.
Former Australia skipper Ponting took a long time to achieve 41 hundreds as captain, setting his mark 324 matches and 376 innings, while its taken Kohli, 31, just 160 matches along with 188 innings more than six decades.
For Evaluation centuries called captain he also moved into spot ahead of Ponting. This was his 20th in 53 Tests, with former South Africa captain Graeme Smith scoring 25 at 109 Test matches.
India batsman Cheteshwar Pujara, who left 55 on day one, had complained about the problem of scoring the ball off under the lights in Eden Gardens.
However, Kohli made it seem easy, putting on numerous partnerships that were essential, such as a stand with immediately spouse Ajinkya Rahane.
The star batsman smashed bowler Abu Jayed for four straight borders in one more before finishing his 194-ball stay with 18 fours .