Mohammad Abbas then removed Kieran Powell to a catch at the wicket in the 14 overs the home side faced in their second innings before the close of play. They will resume on the fourth morning at 40 for one, still needing 41 more runs to erase the first innings deficit with opener Kraigg Brathwaite and Shimron Hetmyer at the wicket.
Deprived of the landmark when stranded on 99 not out in the first innings of the first Test in Jamaica, the Pakistan captain appeared destined to accomplish the feat on this occasion, only to be dismissed in a bizarre manner, triggering a mini collapse in which three wickets fell for 13 runs just before tea.
Having survived an optimistic appeal for LBW against his West Indian counterpart Jason Holder the ball before, Misbah attempted to pull out of the way of the next delivery which lifted sharply and came off the glove for Shai Hope to gleefully hold the catch at second slip.
His typically phlegmatic, unflustered innings lasted almost five hours in which he faced 201 balls, striking two sixes and nine fours. It was also the first time he was dismissed in the series after two unbeaten innings in Kingston.
His surprise demise broke a brisk 57-run partnership with Asad Shafiq after earlier adding 98 with Ali, the opening batsman reaching a painstaking 13th Test century in mid- afternoon before he was caught at the wicket off Devindra Bishoo for 105, the leg-spinner's third success of the innings.
Ali's marathon effort occupied seven-and-a-half hours during which he faced 278 deliveries, stroking just nine boundaries in an innings characterised by considerable discipline and patience.
Buoyed by Misbah's departure, West Indies enjoyed further success just before tea when wicketkeeper-batsman Sarfraz Ahmed became fast bowler Shannon Gabriel's second wicket, edging an attempted drive to Powell at first slip.
Off the very last ball of the afternoon session, Shafiq was ruled leg-before to the miserly Holder, although Pakistan's tail wagged to the tune of another 64 runs after tea, Yasir Shah being last out to Gabriel, who led the home side's bowling effort with four for 81 off 32 overs.
Those eventful sessions after lunch were in direct opposition to the tedium of the morning, where 54 runs came off 26 overs as Ali and Misbah batted with almost exaggerated care on a pitch showing increasing signs of wear and offering disconcertingly variable bounce.