The duo produced a 240-run partnership for the fifth wicket before Shakeel eventually fell for 141, but Rizwan continued to grind down Bangladesh and was unbeaten on 171 when Pakistan decided they had enough on the board.
Bangladesh were 0-27 at stumps with Shadman Islam on 12 and Zakir Hasan batting on 11.
Resuming on 4-158 after a rain-affected opening day, the hosts enjoyed a flawless first session in glorious sunshine as Rizwan and Shakeel primed themselves for big scores against a largely toothless Bangladesh attack.
Rizwan reached his half-century in the 53rd over by steering pace bowler Nahid Rana behind the wicket and followed it up with another upper cut for back-to-back boundaries as Pakistan looked to accelerate.
He caught up with Shakeel thanks to some sublime shot-making as Pakistan went to lunch at 4-256, after making Bangladesh toil on a Rawalpindi pitch that steadily improved for batting as the day wore on.
Having launched Shakib Al Hasan for a huge six over long on after the break to take the partnership past 150 runs, Rizwan brought up his third Test century in style with a boundary off the spinner in his next over.
Shakeel followed suit with his third ton in the longest format and continued to heap pressure on the tourists but the vice-captain was stumped after misjudging a turning delivery from Mehidy Hasan Miraz.
A cramping Rizwan lofted Shoriful Islam over the ropes and brought up his 150 two balls later, before Agha Salman (19) and Shaheen Shah Afridi (29) swelled the total with useful knocks lower down.
