"To all the pollsters out there, you have no idea what you are doing. And to all of the liberals in California and New York, you wasted a lot of money," he said during his victory speech on Tuesday night.
Polls on Tuesday suggested Mr Graham was trailing Mr Harrison by two points going into the election, which is within the margin of error for the polls.
Mr Graham trailed Mr Harrison in fundraising, bringing in only $67m in contrast to his opponent's more than $100m.
Just prior to the election, Mr Graham said he was confident that he would be victorious on election night, despite his polling and fundraising deficit. He said Mr Harrison's challenge was the "greatest" that he'd ever faced.
This will be Mr Graham's fourth term.
The Associated Press called the race for Mr Graham just before 10pm EST.
Mr Graham was able to muster support throughout the state – which is run primarily by Republican elected officials – and benefited among his base by his role in the confirmation hearings of Justice Amy Coney Barrett.
In previous elections, Mr Graham retained his seat handily, defeating challengers by double digit margins.
His victory will be a relief for Republicans hoping to hold control of the Senate. Democrats only need three victories in order to win back majority of the Senate if they also win the presidency. Democrats secured their majority in the House on Tuesday night.
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