India continued their domination on the second day as they added 115 runs to their overnight score 174/3. Kohli and Ajinkya Rahane resumed the innings and went to stitch a crucial 99 for the 4th wicket.
Meanwhile, Rahane brought up his 22nd fifty which was also his fourth consecutive in the longest format. However, he failed to convert it into a hundred as he was taken down by Taijul Islam in the 62nd over. The Indian vice-captain attempted a drive towards the backward point but the ball went into the air and was easily taken by Ebadat Hossain.
Rahane ended up scoring 51; his innings was laced with 7 boundaries.
Despite this loss, the Indian skipper anchored the innings very well and made his outing special by notching up triple figures before going for the lunch break. Kohli got to the landmark, his 70th international ton and 20th as captain, by tucking Taijul Islam for two runs past square leg.
The 31-year old, who now has back-to-back tons at Eden Gardens with the last coming against Sri Lanka in 2017, took 159 balls to get to his century in 234 minutes after being on 59 at stumps on Day 1.
The right-handed batsman shifted gears after getting to his hundred and hit Abu Jayed for four consecutive fours to go into the break on 130 from 187 deliveries. Left-handed all-rounder Ravindra Jadeja was batting with him on 12.
Saturday's ton was Kohli's second against Bangladesh. His first Test century against Bangladesh had come in 2017 when he had scored 204 runs at the Rajiv Gandhi International Stadium in Hyderabad.
This was also the second consecutive century for Kohli at the Eden Gardens. In 2017 when India played last against Sri Lanka in Kolkata, he had scored a 104* in the Test which ended in a draw.