He partnered with Mahmudullah, who smashed an unbeaten 150, for 191 runs on Day 2 at Harare Sporting Club on Thursday.
Zimbabwe were 114 for one loss with Takudzwanashe Kaitano (33) and Brendan Taylor (37) in the middle at the close of play on the second day.
Starting the day on 298 for eight, Mahmudullah registered his career-best innings with two prolific stands after stitching up 132 with Liton Das, who fell agonisingly five runs short of a century.
For the hosts, Blessing Muzarabani grabbed 4-94 while Donald Tiripano and Victor Nyauchi bagged two wickets apiece.
They cracked 28 boundaries in their 276-ball stay as Taskin took on the attack bludgeoning 11 of them, pairing up in the Tigers’ third ninth-wicket Test century.
As the Tigers approached 500, slow left-arm orthodox Milton Shumba went through the gates of Taskin to end the partnership.
He then showed up to bowl the opening over of the Zimbabwe innings.