The Guyana spinner's career-best spell of eight for 49 helped skittle Pakistan for 123 as they chased quick runs to ram home their first-innings advantage of 222.
By the close, West Indies, set a total of 346 to win, had battled to 95 for two, needing another 251 on the final day, which still represents a gargantuan task on a turning pitch against a Pakistan side scenting victory in their 400th test.
An exciting day had started with three more Yasir Shah wickets helping wrap up the West Indian first innings for 357 in just 14.5 overs.
When leg-spinner Yasir, who finished with figures of five for 121, dismissed Miguel Cummins, he reached 100 wickets in his 17th test, becoming the joint-second fastest to reach the landmark in cricket history.
Pakistan did not enforce the follow-on and, preferring instead to pile on the runs with a touch of recklessness, played into Bishoo's wily hands as he recorded the best figures by a West Indian in a test outside the Caribbean.
His performance surpassed Michael Holding's eight for 92 against England at the Oval in 1976.
West Indies lost Kraigg Brathwaite early in their run chase but Leon Johnson and Darren Bravo offered hope with a 60-run stand before Johnson's late dismissal highlighted the magnitude of the Windies' last-day task.
(Reporting by Ian Chadband; Editing by Ken Ferris)
