Pakistan leg-spinner Yasir Shah took all four wickets in the second innings, leaving the West Indies a huge task to avoid defeat on the final day on Tuesday.
Earlier, Misbah was denied his 11th career ton when number 11 Mohammad Abbas was adjudged lbw for 1 to end a valuable 34-run 10th-wicket stand.
The 42-year-old Misbah, who will retire after the current three-test series, is the sixth player to finish a test on 99 not out and the first since South African Andrew Hall in 2003.
Misbah's disappointment at failing to get to his century would have been eased by the fact he helped his team to a first-innings lead of 121.
Misbah patiently faced 223 balls to top-score for Pakistan, while three others also notched half-centuries, including Younis Khan (52), who on Sunday became the first Pakistan batsman to reach 10,000 career test runs.
Shannon Gabriel and Alzarri Joseph were the pick of the West Indies bowlers, collecting three wickets apiece.
Pakistan took command in the final session.
A 50-run second-wicket partnership between Kieran Powell and test newcomer Shimron Hetmyer seemed to set West Indies on the road to safety, but they were both dismissed in quick succession as Yasir weaved his magic.
Yasir then trapped Shai Hope plum lbw for 6 to end the day with figures of 4-33.
(Reporting by Andrew Both in Cary, North Carolina; Editing by Peter Rutherford)
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