Shanto scored two centuries in Sri Lanka earlier this year, but against Ireland in Sylhet he looked more like his earlier self.
Bangladesh opener Joy was adjudged Player of the Match, while debutant Hasan Murad made a significant impact by picking up six wickets across both Irish innings.
Despite the spinners roaring back in the third session with four wickets, Bangladesh's day was defined by a string of missed chances, as the hosts allowed the visitors to wrest back the initiative.
Both players picked up injuries during Friday's T20I against the West Indies in Chattogram, with Sohan twisting his right ankle and Shoriful suffering a right hamstring strain.
