The gold-standard poll, conducted by Verian and released on Monday night, has Mr Luxon's National up two points to 36, compared to Labour, down one to 32.
Combined with coalition partners ACT on 9% (steady) and NZ First on seven (up two), the three parties would enjoy 64 seats in the next parliament if an election was held last week.
The result is welcome news for Mr Luxon, whose government would have been turfed from office based on the last TVNZ poll.
Labour could only hope to tally 58 seats through possible support parties on the left, the Greens (10%, steady) and the Maori Party (3%, down one).
NZ First's 7% is its highest result in eight years, and comes after its leader, Winston Peters, launched a Donald Trump-esque "war on woke".
Mr Luxon's personal popularity remains underwhelming, with just 23% naming the former executive as their preferred prime minister, up 1%.
The alternative, former prime minister Chris Hipkins, enjoyed a three-point bump to 20%.
