Mominul notched up his seventh ton at the Zahur Ahmed Chowdhury Stadium on day 4 to become Bangladesh's highest century-maker in Test cricket, surpassing Tamim Iqbal's the first Bangladeshi batsman
With it, he also achieved another milestone by becoming the joint-fastest to score 3,000 runs for Bangladesh.
Resuming on 47 for 3, the hosts were forced on the back foot after Rahkeem Cornwall trapped Mushfiqur Rahim leg before in the first session.
But a 133-run stand between Mominul and Liton Das helped stretch the Tigers' lead past 350. The partnership was eventually broken when Liton fell for 69 with Mominul also being dismissed shortly afterwards for 115.
The hosts eventually declared at 223 for 8 with a lead of 394 runs to give the bowlers nearly a day and a half to carve out a victory against the West Indies.