Captain Jason Holder grabbed his maiden five-wicket haul as West Indies bowled out Pakistan for 208 and set up a target of 153 runs on Wednesday to win the third and final Test.
West Indies moved to 23 without loss by tea on the fourth day, with Leon Johnson surviving two chances in the slips in Mohammad Amir's first two overs.
West Indies, trailing 2-0 in the series, require another 130 runs for a first Test win against a major team away from home since beating South Africa at Cape Town in 2007.
Holder took 5-30 as Pakistan's second innings was wrapped up after lunch. He claimed the last two wickets to go with his three-wicket burst late on the third day.
Pakistan resumed from an overnight 4-87. Opening batsman Azhar Ali top-scored with 91, and put on 86 runs with Sarfraz Ahmed (42), but both fell to legspinner Devendra Bishoo (3-46) while attempting reckless shots.
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West Indies were sharp in the field, too, with Johnson plucking two brilliant reflex catches at short leg, and Amir was run out by Roston Chase's stunning fielding at long on.
