The poll notably showed voters feel they need to learn more about Harris, while their opinions on Trump are largely set.
In the survey, 28% of likely voters said they needed more information about the Democratic nominee while only 9% said the same about Trump.
The poll indicates that a presidential debate hosted by US broadcaster ABC on Tuesday at 9pm (11am on Wednesday AEST) could be a crucial moment.
Harris will have the opportunity to give more detail on her planned policies as she spars with Trump over the course of 90 minutes.
The race is so close that even a marginal boost for either candidate would be significant.
Since Harris replaced Biden atop the Democratic ticket over the Northern Hemisphere’s summer, she has hit the campaign trail hard but has limited her unscripted appearances and kept interviews with the news media to a minimum.
The key figures from the latest poll are similar to the last comparable New York Times/Siena College survey, released in late July.
In that poll, Trump was also up one percentage point, a difference well within the margin of error.
Polls in the seven key swing states likely to determine the winner of the election have also consistently shown a razor-thin race.