Republican establishment favorite Dan Sullivan will take on vulnerable Alaska Democratic Sen. Mark Begich in the fall after winning his party’s hotly contested Senate primary on Tuesday.

Sullivan, his state’s former attorney general and natural resources commissioner, beat two Republican rivals for the nomination. He faced Lt. Gov. Mead Treadwell and Tea Party favorite and 2010 GOP primary winner Joe Miller.

With 98 percent of precincts reporting. Sullivan had 40 percent of the vote, while Miller had garnered 32 percent and Treadwell placed third with 25 percent. Sullivan led Miller by more than 7,300 votes out of over 90,000 cast. Treadwell already had conceded defeat late Tuesday night, surrounded by supporters, including his three children, at the downtown Anchorage venue where election results were posted.

Sullivan, with millions of dollars at his disposal and major GOP players behind him, had been considered the front-runner in the race. Begich already was treating him as the presumptive nominee, with allies running costly attack ads against him.

Sullivan now assumes the GOP mantle as he competes for a major prize in the Republicans’ midterm playbook. The party needs six seats to flip control of the Senate, and Begich’s is one of their top targets.

Begich won his primary with 97 percent of the vote after facing no real threat. However, the incumbent only received a little over 47,600 votes, just over half the number of ballots cast in the GOP primary.

The primary race represented one of the last chances this year for a Tea Party-backed underdog to take down the favored candidate of GOP powerbrokers.

Leaving nothing to chance, Sullivan spent the last few days covering nearly 900 miles in an RV. He also skipped the last debate to be broadcast statewide to focus on door-to-door campaigning.

Tuesday morning, Sullivan was out with supporters -- including his wife, three teenage daughters and niece -- waving signs along a busy Anchorage street and looking relaxed.

"I'm proud of the campaign we ran," he said. "We have not left any stone unturned."

At a Wasilla-area polling place, Bruce Geraghty, 60, voted for Sullivan. He said he admired Sullivan's military service -- Sullivan is a Marine Corps reservist -- and his efforts to push back against federal overreach while attorney general.

Many of the knocks against Sullivan have come over his residency -- a big deal in Alaska. Sullivan is from Ohio, but his wife is from Alaska and his roots in The Last Frontier date to the 1990s. He left the state in 2002 for stints in George W. Bush's administration and overseas with the military, before returning in 2009 and being appointed attorney general by then-Governor Sarah Palin.

Palin, though, on Friday threw her support behind Miller, who upset Sen. Lisa Murkowski in the GOP primary four years ago, though he ended up losing to her in the general election after she ran a write-in campaign. While he exuded confidence in the race's final days, Miller said late Tuesday afternoon, after being greeted warmly by sign-waving supporters along a busy Anchorage street, that he did all he could do.

"We've left nothing on the table," he said, noting the support he's received has been "phenomenal."

Miller, who spent the campaign painting his opponents as "establishment candidates," said in the waning days of the race that he would support the eventual nominee. That spoke to the state GOP's desire for the party to unite in the cause of defeating Begich and of avoiding a repeat of the divisive 2010 race.

Treadwell had cast himself as the "electable" conservative, in contrast with Miller. Treadwell also set himself in opposition to Sullivan by playing up his decades-long ties to the state, receiving endorsements from four-time Iditarod champ Martin Buser and astronaut Buzz Aldrin.

In the race for governor, Alaska Democrats nominated former Juneau Mayor Byron Mallott to face Republican incumbent Sean Parnell. Mallott, 71, is a Tlingit Alaska Native who once served as mayor of his hometown of Yakutat before going to work for then-Gov. Bill Egan as an aide on local-government issues.

In the race for U.S. House, Republican Rep. Don Young, who is seeking a 22nd term, and 29-year-old political upstart Forrest Dunbar, a Democrat, both won their primaries, while a ballot measure on whether to repeal a new tax on oil companies operating in the state remained too close to call.

Another western state, Wyoming, also held its primary election Tuesday.

In one contest, U.S. Sen. Mike Enzi soundly beat four little-known Republican challengers in his pursuit of a fourth term. They included retired U.S. Air Force Lt. Col. Bryan Miller of Sheridan, a self-employed business consultant and a former advance agent who helped plan visits around the country and abroad by presidents Bill Clinton and George W. Bush.

Also seeking the Republican Senate nomination were self-described soldier of fortune Thomas Bleming of Lusk, oil company worker Arthur Bruce Clifton of Cheyenne and James Gregory of Jackson.

Meanwhile, Rep. Cynthia Lummis won the Republican primary election for Wyoming's lone congressional seat, defeating little-known challenger Jason Senteney and all but assuring she will win a fourth term in November.

Lummis was first elected to the House in 2008. She will face Democrat Richard Grayson, an Arizona resident who has done no campaigning.

The Associated Press contributed to this report.