Mohammad Yousuf, who was unbeaten on 163, continued his superb batting form to help Pakistan reach 396-6 at lunch on the third day on Monday, increasing the home team's lead to 190.
The West Indies scored 206 in their first innings.
Yousuf had an unbroken 111-run stand for the seventh wicket with wicketkeeper Kamran Akmal, who was unbeaten on 61 at the break.
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 captain Brian 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.
Yousuf's marathon 455-minute knock included 19 fours and a six off Mohammed.
Akmal provided him with solid support and hit Fidel Edwards for the eighth boundary of his innings, reaching his fourth Test 50.
Taylor was the pick of the West Indian bowlers with 4-92.