New Zealand was trouble free much of the morning session when Bangladesh struck late to take two wickets as the visitors took a 186-run lead at the break, with the game seemingly drifting toward a tame draw.
Williamson made his total off 150 balls that included two boundaries and one six while Fulton's total came from three boundaries and two sixes off 189 balls before Sohag Gazi (2-61) struck.
New Zealand, resuming on 117-1, looked comfortable batting on a pitch which seemed solid in slightly overcast condition. Play resumed 30 minutes early to make up for the lost time because of rain a day ago at the Zahur Ahmed Chowdhury Stadium.
Williamson, who scored 114 in the first innings, was at ease before he attempted a pull-shot off Sohag Gazi rewarding a catch at forward short leg to Anamul Haque.
Bangladesh was dismissed on 501 in reply to the visitors' first innings total of 469.
