That extended Bangladesh's lead, 27 on first innings, to 179, on course to push for a result on the final day after bad light forced an early end to play with Shanto unbeaten on 58 and Mushfiqur Rahim on 16.
Shanto, who struck a fluent century in the first innings, put on a 105-run partnership with Mominul for the third wicket to keep Bangladesh on the front foot after the hosts slumped to 2-23 in the morning session.
Mominul followed his 91 with 56 in the second innings, extending his rich form with five half-centuries in a row.
"Mominul knows how to handle these situations," batting coach Mohammad Ashraful said. "The partnership of Mominul and Shanto put us ahead today and hopefully we'll set a strong target to push for a victory tomorrow."
Play was stopped for more than three hours because of rain. After resuming at seven for no loss, Bangladesh received an early blow when Mahmudul Hasan was trapped leg-before-wicket by pacer Mohammad Abbas for five.
Pacer Hasan Ali dismissed Shadman Islam for 10, caught by Saud Shakeel at gully after being surprised by extra bounce.
Mominul survived two chances before edging a delivery from pacer Shaheen Shah Afridi.
"We will definitely go for the win," Pakistan all-rounder Salman Agha said. "If they give us around 70 overs and a target near 260, we will absolutely chase it. But I don't think they will take that risk."
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