Updated

Republican establishment favorites dominated virtually across the board in the season's biggest primary day so far, with Senate GOP Leader Mitch McConnell fending off a challenge from his right in Kentucky and Tea Party-aligned candidates falling short in several other states.

McConnell was able to easily best Tea Party-backed challenger Matt Bevin, a businessman who entered the race with high hopes of knocking off the Senate's most powerful Republican. Bevin, though, struggled through a string of controversies and under a withering barrage of McConnell ads -- the GOP leader won by a roughly 2-to-1 margin. His tougher contest will come in the fall, when he faces Democrat Alison Lundergan Grimes.

Several of the primary contests across six states on Tuesday are considered critical to Republicans' hopes of picking up the six Senate seats necessary to take the majority in the upper chamber. In Kentucky and Georgia, Republicans are defending seats they can ill afford to lose.

In Georgia, two GOP establishment favorites -- businessman David Perdue and Rep. Jack Kingston -- are heading to a July runoff after holding back a Tea Party-aligned challenger on Tuesday.

The winner of the July 22 vote will oppose Michelle Nunn, who easily won the Democratic Senate primary, in November.

Establishment-backed candidates have generally fared better than their Tea Party rivals this year, with the exception being Ben Sasse's victory last week in a Nebraska Senate primary. But even among those with party heavyweight backing, the debate is familiar -- with candidates battling for the conservative mantle.

In an interview with Fox News on Wednesday morning, Kingston called Perdue a "moderate flip-flopper," and himself the "consistent conservative."

Perdue, speaking to Fox News shortly afterward, said that's not true and called Kingston a "career politician." He cast himself as an "outsider" eager to address the country's debt crisis and economic problems.

In third place in Georgia, missing out on the runoff, was Tea Party favorite and former Georgia Secretary of State Karen Handel. Reps. Paul Broun of Athens and Phil Gingrey of Marietta were in fourth and fifth, respectively.

The primary has been closely watched nationally. Nunn is considered a formidable opponent, and Republicans are fighting to keep the seat left open by retiring Republican Sen. Saxby Chambliss.

Perdue, a cousin of former Gov. Sonny Perdue, saw his standing rise in recent weeks due in part to TV ads depicting his four opponents as crying babies who had their chance to fix the nation's problems. Perdue, who cast himself as an outsider, chipped in at least $2.1 million of his own money to his campaign.

Kingston, a longtime congressman, dominated in fundraising throughout the GOP race and drew support from dozens of state and local officials. Of the three congressmen, Kingston was considered the strongest and received the backing of the U.S. Chamber of Commerce, which spent nearly $1 million in TV and online ads promoting him.

Handel also sought to claim the outsider mantle. She built momentum in the final month with the help of a comment by Perdue about her lack of a college degree and endorsements from the likes of former Alaska Gov. Sarah Palin, but her lack of money hurt her ability to match Perdue and Kingston in critical TV advertising.

Meanwhile, another race in Oregon could shape up to be a competitive contest in November. On Tuesday night, Dr. Monica Wehby, a pediatric neurosurgeon and political newcomer, beat her Tea Party-aligned challenger to take on Democratic Sen. Jeff Merkley in November.

Wehby beat Oregon state Rep. Jason Congers and three other candidates with 51 percent of the vote. Congers placed a distant second with 36 percent.

Republicans are looking to Wehby pull off an against-the-odds victory in territory where a Republican has not won a statewide election since 2002. However, some believe that first-term incumbent Merkley is vulnerable because he has enthusiastically supported ObamaCare.

In another defeat for the grassroots conservative movement, attorney Bryan Smith also failed to beat Idaho GOP Rep. Mike Simpson Tuesday night. Smith had the backing of the conservative anti-tax Club for Growth, but Simpson won by a double-digit margin.

The Associated Press contributed to this report.