The 58-year-old Graham had about 59 percent of the vote in early returns Tuesday, far more than what was needed to avoid the runoff.
Graham's challengers had argued he was not conservative enough. But Graham, who has been in office since 2002, had a hefty fundraising advantage. He has raised more than $12 million since his last re-election bid in 2008, while none of his opponents passed the $1 million mark.
Graham faces Democratic State Sen. Brad Hutto, as well as Libertarian Victor Kocher, in the November general election.