Dunleavy led Democrat Mark Begich 42.5 percent to 42.3 percent in the poll, which was taken from last Friday through Monday.
Pollster Ivan Moore said the number of people who view Begich positively has grown steadily since September, while those who view Dunleavy negatively has also grown.
“This race might end up being the latest in a long tradition of very close Alaska elections,” Moore said.
Independent Gov. Bill Walker drew 7.7 percent, though most of his supporters know he ended his campaign.
Moore said some of those Walker backers may shift to other candidates – particularly Begich.
“I think they’re in mourning, frankly, and finding it a little bit hard to let go,” Moore said. “I don’t think it’s a permanent state of affairs.”
The poll included Libertarian Billy Toien for the first time. He drew 3.3 percent, while 4.1 percent were undecided.
It was the last Alaska Survey Research poll before the election on Tuesday. Moore didn’t disclose who paid for the polls. He said it was a consortium that included people who supported different candidates.