Andrew Balbirnie's team were in a difficult position after losing four early wickets.
Ireland are back in the hunt to qualify for the Super 12s at the T20 World Cup.
They beat Scotland by six wickets in Hobart this morning.
Ireland were set 177 to win and Curtis Campher was the hero, hitting 72 not out off 32 balls.
His partner George Dockrell was 39 not out.
Captain Andrew Balbirnie is happy Ireland still have life in the competition:
Ireland will face the West Indies in their final group game on Friday morning.
At the moment, the West Indies and Zimbabwe are battling it out.
The Windies made 153 for the loss of 7 wickets from their 20 overs, with Zimbabwe now batting.
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