The survey of 625 registered voters found 45 percent support Democrat Lori Swanson, while 27 percent favor Republican Jeff Johnson. Support for John James of the Independence Party was 2 percent.
But 25 percent remain undecided in the final week of the campaign.
In a similar poll in mid-September Swanson led Johnson by 13 points.
Swanson said the numbers are encouraging, but she's still working on those undecided voters.
"Many people make up their minds in the closing days of the campaign as they really tune in. And I just plan on doing what I have been doing during the last couple of months," she said.
Republican Jeff Johnson agreed there are a lot of undecided voters, but he doesn't buy the other poll numbers.
"They're way off of anything we've seen internally the past three, four weeks," he said. "And honestly at this point in a race like this I don't think polls whether they're our polls or your polls or someone else's matter that much."
The poll's margin of error is plus or minus 4 percentage points.