If she is successful, it would be the first Green electorate seat since Jeanette Fitzsimons won Coromandel in 1999 - and the first without an endorsement from Labour.
"We have defied the odds," co-leader James Shaw told a jubilant crowd of about 400 people at a function centre on Auckland's waterfront.
No minor party had gone into coalition and passed the 5 per cent threshold, he said. Tonight, it was at 7.6 per cent in preliminary results.
"We have made history," Shaw said. "You have made history."
He said the combined left-wing vote signalled a "huge shift in New Zealand society" to progressive politics.
Asked about Labour's ability to govern without the Greens, co-leader Marama Davidson said voters wanted a more progressive government.
"It's pretty clear that people don't want one political party in power," she said.
The co-leaders would not be drawn on negotiations with Labour or what they might seek in terms of ministerial roles.
"Tonight, we celebrate," Shaw said. "Tomorrow, the work begins."
Swarbrick put her extraordinary result down to a surge in youth voting and a relentless ground campaign. She noted that campaign volunteers were reporting that many polling booths had run out of special voting forms today.
"I just want you to know that people told us, 'This cannot be done'," she told supporters last night.
Davidson said no minor party had won a electorate seat without a "deal" with another party.
"It's a historic moment," she said.
On current polling, the party could expand its caucus from eight to 10, bringing in new faces Teanau Tuiono, Dr Elizabeth Kerekere, and Ricardo Menendez March.
The result will come as a relief to the Greens, who had a nervy election campaign in which their vote hovered just above the 5 per cent threshold in most polls.
Shaw made matters worse when he was found to have backed a $12 million grant to a private school - a scandal which would be relatively minor for most parties but cut deeply against his party's firmly held opposition to funding non-state schooling.
As Labour soared in the polls, the Greens warned voters about the risks of a single-party government, saying it was needed to keep Labour honest - especially on the defining issue of the century, climate change.
It pitched itself as the only party willing to take on the broad, structural problems in New Zealand with bold policies, including a radical overhaul of the welfare system and ending coal and fossil fuel use within 15 years.
Its campaign recovered in the last two weeks, possibly because left-leaning voters could see that Labour would ease into government and the Greens were teetering on the threshold for elimination. In a poll just before election day, it rose to 8 per cent of the party vote.
The Greens' proposed wealth tax also received sustained attention in the last week because of National leader Judith Collins' repeated claims that it would be introduced under a Labour-Greens government. It did not appear to do the Greens any damage, and if anything, may have boosted its support.
The policy, one of the key planks of its policy platform, would introduce a tax of 1 per cent on net wealth over $1 million and 2 per cent on net wealth over $2m. It would pay for a guaranteed minimum income and a huge expansion of ACC to cover illness and disability.
The Greens did not take any "bottom lines" into its election bid, instead highlighting six top priorities in the areas of farming, transport, oceans, housing, poverty and energy.
The Greens' party vote is likely to rise a little further because it typically gets a boost from special votes. In 2017, its party vote went from 5.85 per cent on election night (7 seats) to 6.3 per cent (8 seats) after special votes had been counted.
