A potential declaration was put on hold as the visitors allowed Chase the possibility of making his fourth test ton, closing the day on 369 for eight in their second innings.
Chase, 25, played an aggressive innings off 127 balls, including eight fours, as he and Devendra Bishoo added 92 runs for the eighth wicket.
Bishoo was caught for 44 in the last over of the day off the bowling of Zimbabwe captain Graeme Cremer, who returned the best figures of 3-111.
The pair attacked the bowling near the end of the day in a bid to reach respective milestones but were kept in check by the home spinners.
The West Indies were 88-1 overnight, already 148 runs ahead, and moved to 155 for two at lunch with only Kyle Hope losing his wicket for 43.
In the second session, Kraigg Brathwaite fell short of a century as he was trapped lbw by Sikandar Raza on 86 while Shai Hope was lbw to Kyle Jarvis for 44.
The teams are playing a two-test series with both matches in Bulawayo.
(Reporting by Mark Gleeson in Cape Town,; Editing by Ed Osmond)
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