Graham, 58, had about 59 percent of the vote in early returns, far more than what was needed to avoid the runoff. State Sen. Lee Bright came in second, with nearly 14 percent.
Aside from Bright, those arrayed against Graham included Columbia pastor Det Bowers, Upstate businessman Richard Cash and Charleston-area businesswoman Nancy Mace, the first female cadet graduate from The Citadel, South Carolina's military college. Orangeburg County attorney Bill Connor and Columbia lawyer Benjamin Dunn were also seeking the nomination.
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.
The challengers have hammered away at Graham, saying he's not conservative enough for South Carolina. That didn't matter to Ben Lister, a 48-year-old financial planner from Greenville who voted for the senator.
"I know that some people are saying he should be more conservative, but what does that mean?" Lister asked. "I want a politician who actually thinks about the issues instead of going along with the crowd."
Meanwhile, Graham's fellow Republican U.S. Sen. Tim Scott won his primary by a wide margin, setting the stage for South Carolina to elect a black person to the U.S. Senate for the first time.
Scott was appointed to the seat in 2012 after Jim DeMint stepped down, and the general election winner will serve the remainder of DeMint's term.
The Democrats had two primaries of their own, though it's widely expected that the Senate seats will remain in the GOP's hands.
State Sen. Brad Hutto won the nomination for Graham's seat, while Richland County Councilwoman Joyce Dickerson was nominated to face Scott. Dickerson is black, making this South Carolina's first-ever U.S. Senate general election between two black candidates.