West Indies 219 (Shai Hope 90*, Powell 56, Cremer 4-64) and 369 for 8 (Chase 91*, Brathwaite 86, Cremer 3-111) lead Zimbabwe 159 (Bishoo 5-79) by 429 runs.
Bulawayo: Roston Chase and Kraigg Brathwaite made significant contributions with the bat as the West Indies extended their lead over Zimbabwe to 429 on day three of the first Test at Queens Sports Club, Bulawayo on Monday.
After Brathwaite made 86 at the top of the innings, Chase scored an unbeaten 91 to take the West Indies to stumps on 369 for eight.
Although Zimbabwe ended the day with the wicket of Devendra Bishoo for 44 to gain sight of the end of the tourists' second innings, they will now need to achieve a world record chase to win the match.
Captain Graeme Cremer was the most successful bowler on the day, ending with figures of 3 for 111.
Opener Kraigg Brathwaite scored 86 as the West Indies extended their lead. Although Brathwaite was one of four wickets to fall in the second session, his knock set the West Indies on their way to a tea-time total of 244 for six.
The West Indies began the third day on 88 for one, with Brathwaite on 38, and the visitors were forced to make slow but steady progress on a sluggish Queens pitch.
With Brathwaite dropped twice off the bowling of Graeme Cremer, Zimbabwe's only success of the morning came when Kyle Jarvis trapped Kyle Hope lbw for a career-best 43, ending a partnership of 82 for the second wicket.
Hope was replaced in the middle by his younger brother, Shai, who added 67 for the third wicket with Brathwaite.
However Zimbabwe struck back with four wickets in the hour before tea, with Brathwaite trapped lbw to offspinner Sikandar Raza, before Jarvis used the second new ball to dismiss Shai Hope for 44.
Left-arm spinner Sean Williams also enjoyed success with the harder ball, as he had Jermaine Blackwood stumped and Shane Dowrich caught at slip.
With Dowrich falling on the stroke of tea, Roston Chase was left unbeaten on an aggressive 38.
Zimbabwe had bowled the West Indies out for 219 on the opening day of the two-match series, but were then dismissed for 159 on day two.