(CNN) -- In the intraparty battle for the GOP, score Round 1 for the Republican establishment over the tea party.
CNN projects that North Carolina House Speaker Thom Tillis has won the state's GOP Senate primary. Tillis, who was backed by many mainstream Republicans, topped 40% of the primary vote Tuesday, avoiding a runoff in July.
Tillis beat a bunch of more conservative candidates for the chance to face off this November against first-term Democratic Sen. Kay Hagan, who is considered very vulnerable in the general election. Flipping her seat and five others held by Democrats would give Republicans control of the Senate.
In his victory speech, Tillis slammed Hagan's record, tying her to Senate Majority Leader Harry Reid and calling them "an echo chamber for President Obama's worst ideas."
"We need to be clear, it's not the end of a primary, it's really the beginning of a primary mission, which has been the mission all along and that is to beat Kay Hagan and to make Harry Reid irrelevant," he said.
"You know, their failures, both Obama's and Kay Hagan's, are obvious," Tillis added.
"We know a lot of them -- our government is borrowing too much money and it's dangerously in debt to China. Obamacare is not working. And Obama and Hagan's left-wing political agenda is driving up our energy prices and making our country less safe.
"For six years, she's voted with Obama and against North Carolina," he said.
Trailing Tillis is tea party activist Greg Brannon. He enjoyed the support of many tea party groups, other influential conservative organizations and endorsements from the likes of Sens. Mike Lee of Utah and Rand Paul of Kentucky, who joined Brannon on Monday at a rally in Charlotte.
Mark Harris, a prominent Baptist minister who helped drive the 2012 passage of a constitutional amendment that strengthened the state's same-sex marriage ban, is on his way to a third-place finish. Harris was backed by a high-profile fellow pastor, former Arkansas Gov. Mike Huckabee, a 2008 Republican presidential candidate who may run again in 2016.
Since the birth of the tea party movement in 2009, primary challenges from the right have produced major headlines and headaches for the GOP and hurt the party's chances of winning back the Senate from Democrats in the past two election cycles. Candidates backed by the tea party movement and other grass-roots conservatives effectively cost the GOP five winnable Senate elections the past two cycles in Nevada, Delaware, Colorado, Indiana and Missouri.
The establishment strikes back
This election cycle, mainstream Republicans don't want another sequel.
In North Carolina, Tillis won recent endorsements from two high-profile Republicans: 2012 presidential nominee Mitt Romney and former Florida Gov. Jeb Bush, a potential 2016 White House hopeful.
More importantly, while none of the candidates in the GOP primary, including Tillis, raised or spent a lot of money in the campaign, the state House speaker won the backing of the U.S. Chamber of Commerce and American Crossroads, two outside groups that combined have spent millions this cycle to run ads in support of Tillis and other establishment picks that they feel are "electable" come November.
Last week, in what was described as a major buy, the pro-business Chamber launched a television commercial that described Tillis as "a bold conservative who balanced our budget and reduced regulations. A businessman who delivered tax relief."
And Crossroads, the big-spending outside group co-founded and steered by Karl Rove, says it has spent nearly $2 million in support of Tillis. That spending dwarfed the money shelled out by outside conservative groups that backed Brannon.
"It was clear from the start that Thom Tillis is the only proven conservative who can defeat Kay Hagan and take on President Obama's liberal agenda, and tonight's victory is the first step toward making that happen," said American Crossroads President and CEO Steven Law.
Paul was quick to back Tillis.
"Now that the primary is over, it is time for our side to unite to defeat the Democrat who cast the deciding vote for Obamacare, Kay Hagan, in November. I endorse Thom Tillis and look forward to working with him in the Senate," Paul wrote on Facebook.
And a top tea party leader who had backed Brannon sounded conciliatory.
"While we obviously aren't happy with the outcome, we congratulate Speaker Tillis for his win," said Tea Party Patriots' Jenny Beth Martin. "The important thing now is to pick up a U.S. Senate seat that's been in liberal hands for the last six years."
National Democrats argue that the competitive primary pushed Tillis too far to the right for the more mainstream electorate in November.
"Thom Tillis spent this primary moving far to the right, embracing positions that, paired with his record, make him a deeply flawed candidate," said Mike Czin, Democratic National Committee press secretary.
More rounds to come
The voting Tuesday in North Carolina, as well as Indiana and Ohio, kicks off five straight weeks of primary contests that should give a clearer indication of whether establishment Republicans have gained the upper hand against the tea party movement for control of the party.
Two more showdowns between establishment and grass-roots conservatives come on May 20, as the action moves to Georgia and Kentucky, where Senate Republican leader Mitch McConnell faces a long-shot challenge from businessman Matt Bevin, who is backed by many tea party groups and by some influential conservative organizations.
In Georgia, there's a wide-open, free-for-all fight to succeed retiring GOP Sen. Saxby Chambliss. The candidates considered to be more moderate are polling ahead of the more conservative candidates.
Two weeks later, on June 3, the establishment-vs.-tea party faceoff shifts to Mississippi, which is one of eight states holding primaries that day. Six-term Sen. Thad Cochran is facing a serious challenge from state lawmaker Chris McDaniel, but private polling indicates the incumbent has a comfortable lead.
Victories by the more moderate mainstream candidates improve the GOP's odds of recapturing the Senate this November. Democrats hold a 55-45 majority in the chamber but are defending 21 of the 36 seats up in November. Half of those Democratic seats are in red or purple states, such as North Carolina.
Tea party leaders say they've 'changed the narrative'
Leaders of the grass-roots movement disagree that their defeat in the North Carolina Senate primary suggests that the tide has turned against them.
"I think the establishment is taking its victory lap a little early," said Kevin Broughton, spokesman for the Tea Party Patriots Citizens Fund.
And regardless of the outcome of the primary contests, Amy Kremer says the tea party is already victorious.
"The tea party has already won because we have changed the narrative and the political landscape in Washington. Now, both sides of the aisle express concern about our ballooning national debt," said Kremer, who just stepped down as chairwoman of the Tea Party Express and is now helping Bevin in his bid to unseat McConnell in Kentucky.
'American Idol' star holds slim lead
While the Senate contest in North Carolina landed in the national spotlight, some House primaries also grabbed attention.
Two-term GOP Rep. Renee Ellmers faced a primary challenge from a conservative talk radio host because of her being open to considering some limited immigration reform. But she cruised to victory in the GOP primary in the state's 2nd Congressional District.
Her re-election bid may grab even more national attention if former "American Idol" star Clay Aiken wins the Democratic nomination in the district. The race between Aiken and two other Democratic candidates is still too close to call.
With all precincts reporting, Aiken has 40.83% of the vote, with Keith Crisco just behind at 39.4%. If the margin holds up, Aiken would exceed the 40% threshold needed to avoid a runoff.
And while only 369 votes separated them, Aiken's tiny advantage is still outside the 1% margin to stave off a recount.
Aiken told supporters Tuesday night that he was "confident" his campaign would be victorious.
"I said earlier tonight, I sort of preferred when they just open the envelope," he said, a reference to his days on the "American Idol" stage.
In the state's 3rd Congressional District, CNN projects that 10-term Republican Rep. Walter Jones, an anti-war libertarian, has won a hard-fought primary against establishment pick Taylor Griffin, a former George W. Bush administration official who also had a senior role in Bush's 2004 re-election campaign.
In Ohio, Cuyahoga County Executive Ed FitzGerald won the Democratic gubernatorial nomination. FitzGerald, a former FBI agent, mayor and assistant county prosecutor, easily topped Larry Ealy, a former tow-truck driver from the Dayton area.
FitzGerald will now face off in November against Republican Gov. John Kasich, who's running for re-election. The contest could turn into a marquee gubernatorial battle.
House Speaker John Boehner easily won his primary. The 12-term Republican lawmaker, who represents Ohio's 8th Congressional District, a GOP stronghold in the southwest part of the Buckeye State, topped two tea party-backed challengers.
CNN National Political Reporter Peter Hamby contributed to this report.