Taylor added 30 runs to his overnight total to go to lunch on 135 not out, as Zimbabwe overcame an early-morning wobble to reach 285 for six at Harare Sports Club.
Taylor's previous highest in Tests was 117 against New Zealand in Bulawayo in 2011, but he batted through another session and found sturdy support in Graeme Cremer after the dismissals of Elton Chigumbura and Richmond Mutumbami.
Chigumbura offered a tame return catch to Rubel Hossain in the second over of the day to depart for 12, while Mutumbami's whirlwind innings on his debut consisted of 11 runs and 13 deliveries before he was caught behind off Robiul Islam.
Taylor and Cremer batted through the remainder of the session without any real trouble, but the scoring rate remained slow as just 68 runs were added in 30 overs.