The senior batsman survived two dropped chances and had another lucky escape while recording his 20th test hundred as Pakistan took a lead of 59.
Yousuf (107) and Shoaib Malik (61) had put on 125 for the fifth wicket in the last two sessions when play ended 21 overs before the scheduled close because of bad light.
They came together when the West Indies appeared to be clawing back into the match by capturing three wickets in the first session, including two in the space of seven runs.
Pakistan lost Younis Khan (11), Mohammad Hafeez (57) and Inzamam-ul-Haq (0) after resuming on 39 for one.
Yousuf has faced 190 balls and batted for 300 minutes, hitting 14 boundaries in a controlled innings. Malik hit eight fours and a six from 149 balls.
West Indies suffered a costly miss soon after getting rid of captain Inzamam when Daren Ganga dropped a sharp chance off Taylor at gully when Yousuf was on 43.
Yousuf was then very fortunate to survive a stumping appeal against left arm spinner Dave Mohammed with his score on 53.
Soon after flicking Taylor to fine leg for a four to reach his hundred Yousuf miscued a pull shot off the same bowler who floored the high catch in his follow-through.