The two Republicans on the board voted in favor. The lone Democrat voted against.
The move came after Republican lawyer Tom Stark, who lives in Durham County, filed a formal protest alleging "malfeasance" in counting the ballots.
Republicans have raised questions after there were problems uploading the results from five early voting machines on election night.
"This came up on Election Night because Durham was late reporting its early voting. It seems to me that they have a procedural issue in the way they do early voting," said Stark.
WATCH: FULL HEARING
Durham Board of Elections votes to hold hearing on November election results
Officials with the voting machine vendor Election Systems & Software explained that their system has an upload limit of 65,535 votes, and because the early voting machines were used continuously throughout the early voting process, that limit was exceeded.
However, the machines have a tape backup, and the results were manually input into the system. That's why there was a late add of 94,000 votes on election night. That late addition from Durham pushed Roy Cooper slightly ahead of incumbent Pat McCrory in the governor's race when Cooper had been trailing.
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ES&S officials said they were confident in the results shown on the tape, but Stark told board members he wanted a recount.
Friday's formal evidentiary hearing will be to determine if there's probable cause to hold a recount.
Stark also raised questions about the early voting process and the security of the voting machines if they are left locked up in polling places. A Durham election official explained that the machines are locked and only site supervisor has the key. The paper ballots are removed every night, the results tabulated, and then the ballots are brought back to election headquarters and placed in a vault.
Dawn Baxton, the lone Democrat on the Durham Board of Elections, said nothing she heard at Wednesday's hearing convinced her of the need for a recount.
"Consistent and identical to what was actually uploaded to the software that it did capture. So I do not believe there's enough evidence here to proceed with the evidentiary hearing," she said.
But speaking before voting in favor of holding a formal hearing, Durham County Elections Board Chairman William Brian Jr., a Republican, said he doesn't see clear evidence that a recount would change the results, but feels that based on the challenge it is best to go forward with a hearing.
"Our past precedent is we set a fairly low bar as to the question of whether we have an evidentiary hearing," he said. "I think we should err on the side of giving people the opportunity to make their points."
Brian then addressed the larger issues of voting in Durham and race.
"Mr. Stark and others feel that there's something fishy going on here and I understand why they might feel that way. On the other hand, there are others in the community who wonder why it's always Durham that needs to recount its votes," he said.
Continuing, he offered:
"The basis for that argument is this is a community with a large African American population and there is a stigma associated with it somehow that in communities with large African American populations that we have to recount twice because we can't trust them. I don't appreciated that at all. I don't appreciate the comments that have been made to various people in the public that cast aspersions on Durham. Durham has a long history of conducting good elections. We had one bad experience in the last primary, but we've dealt with that."
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Following Wednesday's vote to hold a hearing, the Pat McCrory campaign issued the following statement:
"We are pleased the Durham County Board of Elections decided to move forward with proceedings and hopefully will begin to get answers to the many questions people have. Last night, the State Board of Elections released an affidavit from one of their staff that identified at least 6 errors in Durham's reported numbers, and these public officials must make sure that all of their reported numbers are 100% accurate. We believe it is in everyone's best interest to get to the bottom of what happened so that people can have faith in the results, process and system." - Ricky Diaz, Pat McCrory Campaign Spokesman