As of yesterday afternoon, the country was first on two ranking systems calculated by total medals per head and gold medals per head. Australia was fourth in total medals per head and 24th for gold medals.
New Zealand has a medal for every 633,231 people. Next on the list is Slovenia with three medals, one for every 685,846 people.
The systems are running on several websites, including Medals Per Capita, which also ranks teams by gross domestic product and puts New Zealand eighth and Australia 24th.
Australian broadcaster Channel Nine was criticised on Friday when New Zealand was sitting at 10th on the official medals table and it only showed the top nine countries during a news bulletin.
Sydney Morning Herald sports journalist Brad Walter tweeted: "Can't believe Channel 9 only showed top 9 in medal tally plus Australia, then admitted we didn't want to be reminded NZ were 10th. Ch9 should be showing NZ gold, not pretending it didn't happen."
News website Yahoo!7 asked if it was "time to panic" following New Zealand's rise on the table. Journalist John Edwards said: "It's quite an achievement for the tiny nation and it would be tough to begrudge them their smugness as Australia would react the same if we were to overhaul the mega-nation of Great Britain.
"The Kiwis, however, are not missing their chance to rub it in our 'arrogant' faces with a host of memes mostly done at Australia's expense."
He pointed to "Kiwi criticism" online of Aussie swimmer Emily Seebohm's tears following her silver medal win. At the same time, New Zealand's equestrian team was celebrating winning bronze.
"No one has had the heart to tell the Kiwis that Australia generally aims for excellence and Seebohm has since explained her tears not wanting to seem petulant - she's very proud of her silver medal," Edwards said. "The golds will come in time so let's sit back and appreciate this great moment in sport for our Kiwi cousins. Let's hope we overtake them next week."
Reporter Bren O'Brien of sportal.com.au added: "Australians have always been happy to define ourselves as the little battler punching above our weight, but it's our Kiwi brethren who fare much better in that regard."
Kiwi Flight of the Conchords star Rhys Darby joined in, giving Australia flak on Twitter, saying: "New Zealand are ahead of Australia on the medals table. Geez, I wonder how that must feel, eh Aussie?"
- Alanah Eriksen, NZ Herald