Four converted tries in an opening 12-minute blitz did the damage on Australia's Gold Coast, home to a significant population of New Zealanders who were out in force at Cbus Super Stadium.
Fiji never recovered, leaking eight tries in the first-half and five in a fiery second when a player from each side was sent off.
Centre Casey McLean bagged four of them while Jamayne Isaako booted all 13 conversions.
Adding to Fiji's woes, skipper Apisai Koroisau suffered a suspected broken jaw.
"Pretty special and pleased about how we went about our business," said New Zealand captain James Fisher-Harris.
"Fiji are a good team but I thought we played really well. It was a battle of the forwards."
The Kiwis join already qualified defending champions Australia - who play the Cook Islands later Saturday - in the final four.
Samoa and Tonga meet on Sunday with at least one of them also progressing.
England still have a slim chance but they need Tonga to beat Samoa by at least 46 points to stay in the tournament.
New Zealand, the 2008 champions, went into the game on the back of a statement 82-16 demolition of the Cook Islands, but Fiji were not considered easy pickings.
They hammered the Cooks 40-12 and gave the Kangaroos a scare, eventually going down 36-22.
But it was one-way traffic as New Zealand scored twice inside the opening five minutes.
Halfback Jahrome Hughes sliced through a huge hole to cross under the posts then electric fullback Keano Kini sidestepped a defender to dot down.
A third came from McLean and minutes later fellow centre Dane Gagai pounced in what was quickly becoming a rout.
Fisher-Harris picked up a loose ball near the try-line for their fifth before McLean shrugged off two defenders to bag his second.
They went to the break with a commanding 48-0 lead after Ronaldo Mulitalo and Xavier Willison added two more to pile on the pain.
In an explosive second-half, Mulitalo was sent off for high contact and Fiji's Brandon Wakeham was red-carded for swinging a punch in retaliation as tempers frayed.
Fiji at least held on for 17 minutes before conceding another try when McLean grabbed his third, then he dived over for a fourth with Briton Nikora, Erin Clark and Kini completing the massacre.
The women's World Cup is being held concurrently, with Fiji crushing France 54-6 to set up a semi-final against Australia.
New Zealand face Papua New Guinea later to determine who faces Samoa in the other knockout clash.