First, Abdullah Shafique's unbeaten 160 guided the tourists past West Indies' first innings of 344, then Jomel Warrican took 6-112 to bowl out Pakistan for 387 on Tuesday (Wednesday AEST) and limit the lead to 43 runs.
An opening partnership of 40 between Tagenarine Chanderpaul (17) and Kavem Hodge (34) almost wrote off the lead at Queen's Park Oval before Sajid Khan took 4-32 and Ali Usman 2-29 to reduce West Indies to 6-103 and put Pakistan in control.
Sajid first took the wickets of Chanderpaul and Amir Jangoo (13) before a stubborn partnership between Shai Hope and captain Roston Chase took West Indies to 3-99, giving them hope of reaching the safety of stumps with wickets in hand.
That all changed in the last five overs of the day when Sajid first trapped Hope lbw for 15 and Jayden Seales in the same manner for a two-ball duck. Chase (17) fell to the last ball of the day, losing concentration and providing Usman with a simple return catch.
Pakistan now have the opportunity to wrap up the match on day four and achieve their first Test win away from home since 2023.
The third day also saw Pakistan captain Babar Azam denied his first Test century in four years when he was run out for 88 to end a 183-run partnership with Shafique.
His last Test hundred came in December 2022 against New Zealand in Karachi and his 88 was his highest score in 35 innings since that match.
Earlier, Warrican was splendid with both the old ball and the second new ball as the left-arm spinner had Awais Zafar clean bowled for one when the debutant came out of his crease for a big shot but completely missed the line of the ball.
Shamar Joseph then trapped Salman Ali Agha leg before and Warrican claimed his third of the innings after West Indies took the second new ball when Mohammad Rizwan was bowled for 18.
Warrican then wrapped up the Pakistan tail with three wickets in four balls.
West Indies lead the two-match series after a 90-run victory last week in Tarouba.
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