Toshihiro Aoyama's dipping drive in the 66th minute lit up a pedestrian encounter and sent the J-League champions into the quarter-finals where they will face Egypt's Al-Ahly.
The match was the first in which football's governing body officially used the goal technology although there was little opportunity to test its effectiveness in a game of few chances.
FIFA are using two systems in Yokohama and Toyota City after finally bowing to calls to eliminate 'ghost' goals from the game.
GoalRef, which uses a microchip coil in the ball and low magnetic waves around the goal, was used in Thursday's game with no problems reported.
FIFA said pre-match tests conducted by the referee at both ends of the pitch 100 minutes before kickoff were successful.
Hawk-Eye, widely used in cricket and tennis, will be used in Sunday's quarter-finals in Toyota.
FIFA will be given analyses from the competing companies in January and decide which system to use at next year's Confederations Cup in Brazil.
The technology was not needed as Hiroshima eased past the New Zealanders in Yokohama, although Yojiro Takahagi and Ryota Moriwaki hit the woodwork from long distance after the break.
The Japanese side dominated the game without providing any real threat inside the box.
Dethroned European champions Chelsea and South American Libertadores Cup holders Corinthians join the seven-team competition at the semi-final stage next week.
"The score was only 1-0 but we tried to keep attacking," Hiroshima manager Hajime Moriyasu told reporters. "There was plenty of motivation and effort."
Auckland coach Ramon Tribulietx put a positive spin on the result. "We have to be happy with the way we played," he said. "Don't forget we are an amateur side - it's not easy coming up here to play Hiroshima in Japan."
