The Preston North End forward scored the goal of the game and was the home team's most lively performer, with Blackburn Rovers' Derrick Williams and Sheffield United's Callum Robinson also netting for Mick McCarthy's side.
For all three scorers, the goals were their first at international level.
Youngster Callum McCowatt had given New Zealand a lead on the half-hour mark and he caught the eye more than Burnley's Chris Wood, before the All Whites ran out of steam.
The clash was a warm-up, ostensibly, for the Republic before a crucial EURO 2020 qualifier against Denmark, but it was a fringe team selected by McCarthy.
The home side had the first clear chance but left-back Williams could only produce a shot-cum-clearance from 12 yards after Alan Browne's cross.
New Zealand – appearing after a 525-day absence from the senior international stage – broke through when the host's backline was picked apart and McCowatt slid home a fine cross from the left by Liberato Cacace.
It made for a promising start to the reign of coach Danny Hay, the former Leeds United and New Zealand defender who in August succeeded Fritz Schmid in the post.
However, Ireland ultimately overpowered its visitor. Williams surpassed his earlier wayward effort on the stroke of half-time, heading in Robbie Brady's corner for an equaliser.
New Zealand captain Winston Reid was substituted at half-time, the West Ham defender having made his first senior appearance since March 2018 after a knee injury.
Ireland went in front after 52 minutes when Maguire cracked a 20-yard strike into the top-right corner, and he created a string of chances for others.
Robinson grabbed the Republic's third in the 75th minute, meeting Lee O'Connor's fine cross from the right with a stooping header from eight yards.