With 8 minutes to play, Michelsen put the Black Sticks ahead when the ball fell at her feet in the circle and she sent a lethal reverse shot past the keeper. One minute later a counter attack caught the Irish defence off guard and the Northland combination of Michelsen and Harrison saw the latter put a goal away from close range.
The win saw New Zealand go three wins from three games in the pool phase after overcoming India (1-0) and China (3-1) earlier at the tournament.
The top seeded Black Sticks now face a clash against Korea (bottom of Pool A) in the quarter-finals at 2.30pm today.
All four of today's quarter-finals will be live streamed at hockeynz.co.nz/Video
Black Sticks assistant coach Sean Dancer said Tuesday's match was a tough one against an improving Irish side.
"Ireland were always going to be a strong opponent, and they gave us a really good contest which is a good thing going into the quarter-finals," he said.
"We weren't so good in the first half and we had to weather the storm under pressure. In the second half though our girls really fired up, performed strongly."
Ireland had silenced the crowd in the ninth minute after a NZ defensive error and an ensuing rush into the circle, where Nicola Evans knocked home a goal past goalkeeper Georgia Barnett.
Hawke's Bay Cup - today's quarter finals:
* 10am Australia (1st Pool A) vs India (4th Pool B)
* 12.15pm China (2nd Pool B) vs Canada (3rd Pool A)
* 2.30pm Black Sticks (1st Pool B) vs Korea (4th Pool A)
* 4.45pm Japan (2nd Pool A) vs Ireland (3rd Pool B)
