The assembled school sang Tutira Mai and followed it up with a fierce haka, which was videoed.
A staff member entered the performance into a national competition while the video was posted on the school's Facebook page along with a challenge to other schools to get behind the All Blacks.
On Tuesday, Mr Kaua received a phone call to say the school had won.
"We get two tickets to the All Blacks private training session on Thursday, two more tickets to the captain's run on Friday, and two tickets to the test match on Saturday."
One student was chosen at random to attend each of the two training sessions and the test match - Chey Winterburn, Kane Hinga and Hinemoa Hall. Each will be accompanied by staff.
Hinemoa captains the City College girls' rugby team and was selected this year to attended the Hurricanes development squad.
Mr Kaua said only three students would benefit but the whole school "rose to the challenge" and put on a superb, and completely impromptu, performance.
He was hoping the students attending the two training sessions might be able to catch up with City College old boy and current All Black Waisake Naholo.