Updated

South Carolina Sen. Lindsey Graham fended off a field of Tea Party-backed challengers Tuesday night to win the state’s Republican primary and the right to try for a third term in November.

The 58-year-old Graham was declared the winner by the Associated Press after taking about 57 percent of the vote with 96 percent of precincts reporting. State Sen. Lee Bright came in second, with about 15 percent.

Graham, considered one of the most vulnerable incumbent Republican senators in this year's cycle, needed at least 50 percent of the vote to avoid a runoff against one of his six opponents, all of whom had criticized him for not being 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 will face Democratic state Sen. Brad Hutto and Libertarian Victor Kocher in November in the largely conservative state.

Arkansas, Maine, Nevada, North Carolina, North Dakota and Virginia also held primaries Tuesday.

In an unusual situation, South Carolina held two Senate primaries Tuesday.

GOP Sen. Tim Scott, appointed in 2012 after Sen. Jim DeMint resigned, also won his primary election. That sets the stage for South Carolinians to elect a black person to the U.S. Senate for the first time.

GOP Gov. Nikki Haley did not have a primary challenger and will face state Sen. Vincent Sheheen in November in a rematch of the 2012 race.

Graham entered his race facing sharp criticism for supporting comprehensive immigration reform and voting to confirm both of President Obama’s Supreme Court nominees, Elena Kagan and Sonia Sotomayor, both considered liberal justices.

The conservatism critique 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."

However, Graham has also been among the president's harshest critics on foreign policy. He and fellow Sens. John McCain, R-Ariz., and Kelly Ayotte, R-N.H., have called the president's plan to withdraw virtually all U.S. troops from Afghanistan by 2016 a short-sighted mistake that would embolden enemies.

During an emotional victory speech in downtown Columbia, Graham thanked his supporters and pledged to move forward on several key issues and work toward winning a Republican majority in the U.S. Senate.

"To the people of South Carolina: Thank you. I will not let you down," he said.

Graham's other opponents included Columbia pastor Det Bowers, Upstate businessman Richard Cash and Charleston-area businesswoman Nancy Mace, the first female cadet to graduate from The Citadel, South Carolina's military college. Orangeburg County attorney Bill Connor and Columbia lawyer Benjamin Dunn were also seeking the nomination.

The Associated Press contributed to this report.