The Windies came into the penultimate day staring down the barrel at 103-6, only a lead of 60 runs with four wickets of their second innings remaining.
The Pakistan bowlers did not relent as the hosts were bowled out for 117, leaving the visitors a target of just 75 to win the second Test, with the home team suffering a blow as opener Brandon King could not bat due to injury.
It was the Pakistan spinners that did most of the damage in the second innings with both slow-bowlers, Sajid Khan and Usman Ali, both picking up four wickets.
Pakistan lost Imam-ul-Haq early in the run-chase, caught at slip off seamer Jayden Seales, but Azan Awais and first-innings centurion Abdullah Shafique steadied the ship.
West Indies were bowled out for 344 in their innings before the visitors replied with 387, with Shafique (160 not out) and captain Babar Azam (88) the top-scorers.
The third innings of the game was the turning point though as the home batters just could not cope with the spin twins of the Pakistan bowling attack.
Pakistan will now turn their attention to a tour of England whwre they will start with a three-match Test series on 19 August at Headingley.
Joe Root will return to the captaincy when England begin their three-match Test series against Pakistan later this month, with selectors announcing a 16-man squad for the opening two fixtures.
West Indies Test captain Roston Chase admitted it was a combination of team balance, a spin-friendly pitch and tactics that led to their eight-wicket loss to Pakistan.
In a near-perfect day of Test cricket that ebbed and flowed, Pakistan found themselves on top at the end of play on day three in Port of Spain in the West Indies.
Pakistan seized control of the second Test by stumps on day two, reaching 266 for 2 in reply to West Indies' 344 to trail by just 78 runs after producing their strongest batting display of the series.
