England had been bowled out for just 275 in their first innings, with Tim Southee taking 6-43, in reply to New Zealand's 378 featuring debutant Devon Conway's 200.
Shanto took his maiden Test century to 163 while Mominul weighed in with 127 as they shared Bangladesh's best ever partnership for the third wicket in Tests.
Up to 55,000 fans, half of capacity, will be allowed at the stadium, which was renamed after India's prime minister hours before last week's third Test.