Mr Luxon's National party is in a tight race against the Labour-led left in the November 7 election.
Polling shows a deadlock between National-led coalition and the three opposition parties after a campaign dominated by cost-of-living issues.
Mr Luxon said that rather than be blamed for those economic struggles, the turnaround job was underway and would take flight in a second term.
"This is a serious election and there is a lot at stake. And the outcome, I think, will shape New Zealand for years to come," he told an election-eve party in his east Auckland electorate of Botany.
"We can stick with the plan that's working under National, a plan to manage the economy responsibly meaning more jobs, better wages, more opportunities, and a more secure future for Kiwis.
"Or we can risk it by going back to a Labor-led coalition propped up by Chloe Swarbrick and the Greens.
"That is why National is asking for three more years to finish the job. Let's not leave it half done."
The final poll of the campaign, released by Wellington newspaper The Post on Friday morning, suggested Labour eking out a lead over its major party rival.
Labour polled 30.7 per cent, with National on 26.4 per cent - which would be among its worst electoral performances in the party's 90-year history.
The Greens are on 13 per cent, right-wing government parties NZ First and ACT are on 12 and 9.8 respectively, with the Maori Party on two.
It is yet another poll which shows neither the left or right with a majority but instead new teal force Opportunity calling the shots in post-election negotiations.
Qiulae Wong's party polled 5.1 per cent, and on that figure, would send MPs to parliament for the first time and hold the balance of power.
Its support is uncomfortably close to missing the all-important threshold of five per cent to return MPs: should it receive 4.9 per cent of the vote, it will miss out entirely.
The election's tightness is leading to concerns that the next government could be decided by tactical voting, where voters split their support among parties to generate an undemocratic outcome.
On Thursday night, representatives of the top seven parties engaged in the final TVNZ debate before the Saturday's election.
With one million viewers expected to have tuned in - or 25 per cent of the electorate - it may have been the last chance for parties to convince undecided voters.
To that end, Ms Wong might have won the debate by attending and getting in front of a large audience.
Ms Wong's party welcomes comparisons to Australia's teal movement, even using the same colour, and champions the same issues: integrity, climate and bipartisanship.
Labour looms as a likely beneficiary from Opportunity's entry to parliament, given National has ruled out forming a coalition with them.
Labour leader Chris Hipkins, who has been focused on cost-of-living issues in opposition, finished his campaign with calls to improve the health system.
"This government are in complete denial about the mess they have made of public health in New Zealand. Labor has a plan to fix it," he said.
Mr Hipkins wrapped up his campaign in his hometown of Wellington, while most candidates chased votes in Auckland.
Mr Luxon finished a three-day road trip from the capital to Auckland, where most other party leaders were chasing votes.
With major parties polling at historically low levels, at least three parties are on track to record their best-ever vote share in this election.
They are Opportunity, the right-wing free-marketers ACT, and the Greens.
Veteran populist, NZ First leader Winston Peters, voted in Ponsonby as he seeks a 14th term as an MP.
The 81-year-old offered a damning verdict on the campaign, which he believed was devoid of serious policy discussion.
"It's the worst of my career ... a shambolic circus," he said.