The Windies lost Daren Ganga (five) and Chris Gayle (11) before reaching 28-2 at tea on the third day after Pakistan piled on 485 in their first innings, including a masterly knock of 192 from Yousuf.
The visiting side, who need another 251 runs to avoid an innings defeat, will now rely on their captain Brian Lara who was unbeaten on eight at the break on Monday. The other not out batsman was Ramnaresh Sarwan on four.
Earlier Yousuf, who was not out on 107 overnight, continued an in-form run to pile the agony on the tourists. His eight-hour, 21-minute-long innings finally ended when he missed a flighted delivery from off-spinner Chris Gayle and was stumped.
Yousuf hit 24 boundaries and a six on his way to his 20th Test hundred and added 139 runs for the fifth wicket, with Shoaib Malik (69), then another 148 for the seventh wicket with Kamran Akmal (78).
Resuming at 265-4, Shoaib Malik was caught at short mid-wicket off a miscued on-drive for 69, and in the next over Abdul Razzaq (five) edged Taylor for a regulation catch behind the stumps to leave Pakistan at 285-6.
Taylor's fellow paceman Corey Collymore could have dismissed Yousuf, had Lara held on to a low catch in the slips when the batsman was on 114.
Yousuf also survived a close run-out call on 143, when Dave Mohammed failed to hit the stumps from the covers with the batsman well short of his crease.
He took full advantage of the lapses and reached 150 with a push to cover for two off Mohammed.
Akmal provided him with solid support and hit Fidel Edwards for the eighth boundary of his innings, reaching his fourth Test 50. Gayle had Akmal caught at mid-on before he dismissed Yousuf.
Last pair Danish Kaneria (23) and Umar Gul further agonised the tourists by adding 39 runs before left-arm spinner Mohammed wrapped up the innings.
Jerome Taylor finished with 4-115 and Mohammed took 3-98.