The 16-year-old died after he was injured at the party on Medbury Tce in Fendalton on Friday night.
Two other victims were also stabbed - one aged just 14 and the other 17 - and are in a serious condition in Christchurch Hospital.
Police have said the party was attended by about 80 youths, some of which were not invited.
It was held at a house rented through Airbnb on Medbury Tce, described as "a quiet cul-de-sac".
Today, as the hunt for his killer ramps up, Zion's family has spoken for the first time.
"Zion's family would like to thank the wider Christchurch community for the support and aroha they have been shown over the past few days," they said in a statement provided by police.
"This continues to be an extremely difficult time for them as they plan ahead for Zion's funeral on Friday.
"At this time, they are requesting privacy to focus their efforts on the funeral preparations.
"They would like to thank those who have come forward to share information with police and encourage anyone who is yet to come forward, to please do so."
Zion's partner also posted a tribute online.
"I feel so lost, nothing will ever be the same," the post read.
"It feels like I lost the best part of me. You hold a place in my heart no-one could ever replace.
"You were my world bro, you made everything feel so much better.
"I feel like I can’t even stand on my own two feet any more.
"Fly high my love, light up the sky."
The investigation, dubbed Operation Medbury, is ongoing and today police said investigators "continue to make positive progress" following the death of Zion and the serious assault of two other young men.
"Thanks to the large number of co-operative people who've come forward, we're confident we have a clear picture of what happened that night on Medbury Terrace," said Detective Inspector Michael Ford.
"Investigators have also received both CCTV footage and cellphone images which they are now in the process of reviewing.
"We would like to thank all of those people who acted on our request for information.
"This has proved to be extremely valuable."
Medbury Tce remains cordoned off while police complete the final stages of the scene examination.
Ford said police would continue to provide updates and support to both Zion's whānau and the two other victims and their families.
Can you help? Contact the Operation Medbury team
Information can be provided via 105, quoting Operation Medbury, or anonymously through Crime Stoppers - 0800 555 111.
You can also view this release, including any additional images, on the NZ Police app or here.
