Yousuf's 192 helped Pakistan score 485 in their first innings, before they caught the tourists napping at 74-3 at close on the third day at Gaddafi stadium on Monday. The West Indies had made 206 in their first innings.
The Windies, who need another 205 runs to avoid an innings defeat with seven wickets in hand, now look to their captain Brian Lara who was unbeaten on 28 at close with nightwatchman Fidel Edwards not out on five.
Lara, whose first two scoring shots were boundaries, survived some anxious moments before bad light stopped play 20 overs early.
Scorecard of Day 3
The West Indies had a disastrous start to their second innings when Daren Ganga failed to beat a throw by Imran Farhat from square-leg after being sent back by Chris Gayle in the fourth over.
Gayle followed his fellow opener as he edged paceman Umar Gul to wicket-keeper Kamran Akmal after scoring just 11 to leave the West Indies tottering at 20-2.
Lara and Ramnaresh Sarwan took the score to 56 when Gul struck again by trapping Sarwan in front of the wicket for 23. However, television replays showed Sri Lankan umpire Asoka de Silva again faltered with the ball hitting the batsman high on the pads.
Earlier Yousuf, who was unbeaten 107 overnight, continued his good batting form to pile the agony on the tourists.
Yousuf hit 24 boundaries and a six in his 20th Test hundred and added 139 runs for the fifth wicket with Shoaib Malik (69) and another 148 for the seventh wicket with Akmal (78).
His eight-hours and 21-minute-long innings finally ended when he missed a flighted delivery from off-spinner Gayle and was stumped by wicket-keeper Denesh Ramdin.
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.
Malik, who missed Pakistan's tour of England earlier this year with an elbow injury, hit ten boundaries in his 155-ball knock and provided able support to Yousuf after Pakistan lost their way at 140-4 on Sunday.
West Indies applied pressure but once again luck deserted them.
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 left-arm spinner Mohammed. He then hit Mohammed for six over long-off.
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 by Lara to finish with 2-24.
Akmal hit 13 boundaries during his 159-minute stay at the crease.
Last pair Danish Kaneria (23) and Umar Gul (16) further agonised the tourists by adding 39 runs before Mohammed wrapped up the innings by dismissing Kaneria caught behind.
Jerome Taylor finished with 4-115 and Mohammed took 3-98.
However West Indian coach Bennett King said his team were not out of the running.
"The match has not finished as yet. I think if we put some runs on the board we can put pressure on Pakistan," said King.
King added that he was not surprised by Pakistan's strong bowling attack despite the loss of key pacemen Shoaib Akhtar and Mohammad Asif due to doping bans.
"Pakistan's reserve bowlers didn't surprise me because they are used to bowling under these conditions," said King, an Australian who took over as West Indian coach two years ago.