As of 11:37 p.m. Eastern with 95 percent of the state reporting, Trump had about 51 percent of the vote or 2,296,492 ballots, while Clinton had 46 percent and 2,053,568 votes.
In 2012, Mitt Romney won the Tar Heel State by 2 percentage points. Trump headed into Election Day with a slightly narrower margin of about 1 point, according to a RealClearPolitics average of recent polls, but Clinton led the race by as much as 3 points in October.
Trump and Hillary Clinton fought a tough fight for North Carolina's 15 electoral votes, overtaking each other multiple times in the polls over the course of the last several months. The two candidates stopped in capital Raleigh on Monday, campaigning in the critical state right up to Election Day.
Burr had a 2-point lead ahead of Election Day, according to RealClearPolitics' average. That spread was far narrower than the one he had in 2012, when he had a 12.8 lead in the polls, and won re-election by 12.1 points.
When it comes to national elections, North Carolina was once considered a Republican stronghold, but the state's changing demographics — it has a rising number of transplants from the Northeast and Midwest, as well as a growing Hispanic population — helped flip the state in 2008 for Barack Obama.
On Tuesday, Durham County switched from electronic poll books — the list used to check voter registrations — to paper ones amid technical issues. A spokeswoman confirmed to CNBC that the county's board of elections subsequently asked for permission to keep polls open until later. Durham County has a substantial African-American population.
As a result, the state board of elections extended voting time by up to an hour in a handful of precincts, mostly in Durham County.
Earlier, NBC News reported that some voters were told to come back later after precincts ran out of paper "Authorization to Vote" forms.
"This is not acceptable," Allison Riggs, a lawyer with the Southern Coalition for Justice, wrote to the State Board of Elections.
Patrick Gannon, spokesman for the state board of elections, said that according to state law, extensions have to be granted on a precinct by precinct basis, not countywide. Evidence of delays would also have to be submitted by precinct, which the county said it is working on. The state board would then meet by phone to consider the evidence.
The news comes amid ballot-access advocates' concerns about potential efforts to suppress voter turnout.
The Justice Department has accused the state's GOP-dominated legislature of intentionally making it harder for African-Americans to vote in North Carolina, and federal judges have twice ruled against the state in voting rights cases since July.
In July, a U.S. Court of Appeals struck down provisions of a voting law in the state after determining Republican lawmakers passed the measure to "target African-Americans with almost surgical precision." NBC News reported that counties with reduced early voting sites and restrictive schedules saw declines in black turnout.
This is breaking news. Please check back for updates.
— CNBC's Scott Cohn and NBC News contributed to this report.