After his career-best 171 in the first innings, the 27-year-old followed it up with an unbeaten 102 in the second to become the third Zimbabwe player to score two centuries in a Test.
Taylor`s name now sits alongside the Flower brothers, Andy and Grant, and his contribution helped the home side get to 227 for seven declared in Harare.
They lead by 478 overall and now have the best part of two days to take the 10 Bangladesh wickets they need for victory.
Starting the day on 187 for seven their progress was hardly quick but, with a commanding lead already assured, Taylor gave himself enough time to reach his milestone.
His knock came from 146 balls and contained seven boundaries - two of them maximums - while support came from Keegan Meth who made an unbeaten 31 from 62 balls.