Shai Hope, coming in to bat at number four, was unbeaten on 90 off 201 deliveries as West Indies, who won the toss, opted to bat were bowled out for 219 in 82.5 overs in their first innings. His teammates let him down, though, and he finished 10 short of a third century in his last five innings.
West Indies and Zimbabwe both threw punches in an engaging contest, but the Zimbabwe spinners came to the fore after tea with seven wickets in the session. Wicketkeeper Regis Chakabva was also superb behind the stumps with two catches and a stumping.
And they were in further trouble in the third over following the hour mark when Kyle Hope was adjudged caught at the wicket on review for 16, giving debutant all-rounder Mire his first wicket in Tests at 35 for two.
Electing to bat first, the West Indies did not get off to the best of starts as opener Kraigg Brathwaite was caught behind off the bowling of Kyle Jarvis, who was returning to worldwide cricket after ending his Kolpak deal with Lancashire.
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But he lasted just 14 more balls before edging a sweep at Cremer onto his pad and into the hands of Craig Ervine at short leg, to depart in the second over after the drinks break after facing 133 deliveries and striking six fours.
Kieran Powell and Shai stabilised the innings with a 75-run partnership, during which Powell brought up his half-century.
Cremer was the pick of the bowlers with four wickets, while Williams snapped up three, and Jarvis, Mire and Raza claimed one wicket each. The left arm spinner had his second wicket, West Indies skipper Jason Holder leg before wicket for eight, the tourists seven down for 212. It was all over for the West Indies in the very next ball, Shannon Gabriel gone for a first ball duck, Cremer needing Ervine's assistance once again to effect th dismissal.
Hope and wicketkeeper Shane Dowrich (11) attempted a fix job in a 23-run, sixth wicket stand which took their side past the 200-run mark.