Pakistan resumed after lunch on 267/8 in reply to West Indies first-innings total of 311 but managed to add only 15 more runs before being dismissed in 80.1 overs.
The visitors suffered an early setback in the second session when Greaves dismissed Mohammad Abbas for a duck to complete his first five-wicket haul in Test cricket.
Khurram Shahzad provided some lower-order resistance with 19 off 36 balls before falling to veteran pacer Kemar Roach.
Greaves led the West Indies bowling attack with outstanding figures of 5/27 in 11 overs. Roach and Shamar Joseph picked up two wickets each, while Jayden Seales claimed one.
Earlier in the day, Pakistan resumed their innings at 199/3, with overnight batters Shan Masood and Salman Ali Agha frustrating the West Indies bowlers.
The pair added 47 runs for the fourth wicket, during which Masood reached his seventh Test century and his first since being replaced as Pakistan s Test captain by Babar Azam.
Shamar Joseph broke the partnership by bowling Agha for 20 with a late-swinging delivery that clipped the top of off stump. The all-rounder struck three fours in his 60-ball innings.
Greaves then dealt Pakistan a major blow by dismissing centurion Masood, who top-scored with 109 from 184 deliveries, including 12 boundaries.
The all-rounder continued his impressive spell by removing Aamir Jamal for three, debutant Ali Usman for a duck and Mohammad Rizwan for 12, reducing Pakistan to 259/8 before wrapping up the innings after lunch.
