If Haley, a 38-year-old first-generation American of Indian descent, defeats Democrat Vincent Sheheen in November, she also would be the state's first minority governor, The New York Times reported.
Haley won despite being dogged during the primary campaign by allegations of marital infidelity, which she has denied.
Haley and Sheheen are vying to succeed Gov. Mark Sanford, a Republican who couldn't seek another term because of state limits.
Veteran politician Elaine Marshall defeated former Army prosecutor Cal Cunningham for the Democratic nomination for U.S. Senate in North Carolina, the Times reported. Marshall will face incumbent Republican Richard Burr, who is seeking a second term.
In South Carolina, six-term 4th District GOP Rep. Bob Inglis was defeated handily by prosecutor Trey Gowdy. Inglis became vulnerable because of his support of the banking industry bailout, the Times said.
In the 1st District Tim Scott won the Republican nomination in his bid to become South Carolina's first black congressman in more than a century. He beat Paul Thurmond, son of the late Sen. Strom Thurmond. If Scott wins this fall, he would be the first black Republican to serve in Congress since Rep. J.C. Watts of Oklahoma left in 2002, CQ Politics reported.
In Mississippi, former police officer Bill Marcy of Meridian defeated teacher Richard Cook of Byram in a Republican runoff in the state's 2nd Congressional District, WTVA-TV, Tupelo, reported. Marcy, who garnered about 60 percent of the vote Tuesday, takes on eight-term Democratic incumbent Bennie Thompson and the Reform Party's Ashley Norwood in November.
Voters also went to the polls in Utah Tuesday. Republicans there were deciding whether Tim Bridgewater or Mike Lee will be their party standard-bearer in November, having ousted veteran U.S. Sen. Bob Bennett during the state GOP convention.
Bennett was turned aside by a more conservative bloc at the party convention -- in part because of his vote for the financial bailout in 2008. After considering a write-in campaign, Bennett said such a bid would fracture the Utah Republican Party further, take a financial and emotional toll on his family and friends, and add to the "toxic" environment percolating in his home state.
Swim Week Miami Beach 2014 [PHOTOS]