He cracked 14 fours in his fourth Test century as Pakistan reached 295-3 in their first innings at tea in reply to Bangladesh’s 135, for a 160-run lead with with seven wickets in hand.
Younis Khan was unbeaten on 25 at the break with skipper Misbah-ul-Haq 16 not out as the tourists added 163 runs to their overnight total of 132 for no loss.
Hafeez, whose previous best was 119 against Zimbabwe in Bulawayo this year, was unlucky to be adjudged leg-before off left-arm spinner Elias Sunny, as TV replays suggested he had inside-edged the delivery on to his pad.
Bangladesh struggled for success on an easy-paced pitch as they took only three wickets in the first two sessions, with off-spinner Mohammad Mahmudullah, paceman Shahadat Hossain and Sunny taking one wicket each.
The hosts took the second new ball immediately after it was due and Shahadat had a chance to dismiss Younis on 15, but Sunny dropped the catch at deep square-leg.
Bangladesh also let off Misbah on five when the batsman edged paceman Rubel Hossain, but Shahriar Nafees failed to hold on to the ball at second slip.
Hafeez put Pakistan in a strong position when he added 164 for the opening wicket with left-handed Taufeeq Umar (61) and 56 for the second wicket with Azhar Ali (26).
Hafeez, 74 overnight, reached his century in the morning session with an aggressive shot when he drove Mahmudullah through the covers for a four.
The hosts broke the opening-wicket stand in the day’s 16th over when Mahmudullah trapped Umar leg-before after the batsman had added eight runs to his overnight score of 53. Umar’s 164-ball knock contained eight fours.
Bangladesh got their second wicket when Shahadat had Azhar caught behind.
