The left-hander resumed the day on 85 and showed remarkable composure throughout his innings before reaching the three-figure mark in the 51st over. Awais brought up his century with a single off the fifth delivery from Nahid Rana, becoming only the 14th Pakistan batter to score a hundred on Test debut.
His achievement was even more significant as he became just the third Pakistan player to register a Test century on debut away from home.
Bangladesh eventually found the breakthrough through Taskin Ahmed after Awais attempted an expansive shot outside off stump. The right-arm pacer induced an outside edge with a short-of-a-length delivery, and captain Najmul Hossain Shanto completed the catch at slip.