With a 31-run win over Zimbabwe, West Indies improved their chances of qualifying for the Men’s T20 World Cup.
With 10 balls remaining in Hobart, fast bowler Joseph took 4-16 to help Zimbabwe be dismissed for 122.
The West Indies had earlier reached 153-7 after losing four wickets for 11 runs in the middle of the innings.
After Ireland defeated Scotland earlier in the day, all four teams in Group B now have two points.
Ireland takes on West Indies on Friday, followed by Scotland taking on Zimbabwe.
The top two teams in each group will advance to the Super 12s, which begin on Saturday. The winner of Group A and the runner-up of Group B will be placed in a group with England.
With rain expected in Hobart on Friday, if both matches are rained out, Scotland and Zimbabwe will advance.
Scotland leads the table with a higher net run rate than Zimbabwe, with the West Indies third and Ireland fourth.