The Kiwis thumped the Scots 52-33 in a 13-try thriller in Argentina.
"Unfortunately, there was an issue with the international satellite provider which meant that we did not receive a stream to show to our customers," Spark said in a statement to the New Zealand Herald.
Customers trying to watch the match between 6.30am and 7.15am were affected. This also affected other international providers trying to stream the game around the world, a Spark spokeswoman said.
Other sporting content live on the platform at the time, including the Canadian Grand Prix Qualifier and the U20 England v Italy, was unaffected.
Spark apologised for the disruption and said a complete version of the NZ v Scotland match will be available to watch on demand this morning.
One rugby fan who went to watch the game using Spark Sport's free trial expressed frustration and concern about future sporting events including the 2019 Rugby World Cup.
"It's 06.42 and I'm staring at a Spark Sport bulletin on my screen 'sorry for the interruption. The team are working on a fix'.
"In a few days I'll be paying for this service, but every time I use it there seems to be some kind of issue," said the man, who wished to remain anonymous.
Customers can pay $80, rising to $90 for those who wait until September for the Rugby World Cup Tournament pass, which kicks off on September 20.
Spark has stressed that its service has been in a "beta" or test phase that was always going to involve ironing out a few bugs - and that it has worked smoothly most of the time so far.
However users have taken to social media to sound-off about bugs that have affected Spark Sport Formula One and hockey coverage at times.
The telco is offering pubs and clubs a Spark Sport subscription at a household rather than commercial rate, and is making all the All Blacks pool games, plus the semis and final, available through free-to-air partner TVNZ. The pool games will screen on a one-hour delay.
TVNZ will also screen the opener, plus the All Blacks presumed quarter-final on a one-hour delay.
