Burr comes out ahead of the former state representative, 48-47, among likely North Carolina voters.
Quinnipiac's previous September poll also showed a tight race for the North Carolina Senate seat. In that poll, the two candidates were tied at 46 percent.
The Quinnipiac University poll was conducted via live telephone interview from Oct. 20-26 among 702 likely North Carolina voters, and has a margin of error of plus or minus 3.7 percent.
TPM's PollTracker Average for the U.S. Senate election in North Carolina shows a tossup, with Burr leading Ross, 45.9 to 44.