Republicans’ hopes of taking back the Senate received a big boost in primary elections Tuesday, with Minority Leader Mitch McConnell (Ky.) easily winning and other candidates favored by the party establishment beating back tea party challengers.

After years of intraparty turmoil that cost Republicans key races, voters this year are coalescing around the GOP’s strongest candidates ahead of November’s general election, when control of the Senate during President Obama’s final two years in office will be up for grabs.

On Tuesday, the most consequential day of voting so far this year, Democrats were left disappointed. GOP Senate candidates prone to making controversial statements lost to better-financed, more disciplined rivals with the potential to capi­tal­ize on Obama’s unpopularity and the troubles with his signature health-care law.

Nowhere was this more evident than in Kentucky and Georgia, the only two states where Democrats think they can win Senate seats held by Republicans. Democrats had hoped McConnell would emerge from the primary campaign badly bruised, if not defeated, but he prevailed Tuesday largely unscathed and conservative groups quickly called for party unity.

And in Georgia, Democrats were banking on Republicans nominating a candidate so far to the right that he or she would alienate suburban centrist voters. But the two contenders considered to have the broadest general-election viability — businessman David Perdue and Rep. Jack Kingston — advanced to a July 22 runoff, complicating Democrat Michelle Nunn’s path to victory.

Upcoming primary elections are likely to yield similar results. The tea party’s best and perhaps only remaining chance for an upset is in Mississippi, where support for Sen. Thad Cochran seems shaky, although his conservative challenger, state Sen. Chris McDaniel, has stumbled.

In Kentucky, McConnell’s weak poll numbers and voters’ overwhelming dissatisfaction with the Senate he helps lead made him particularly vulnerable to a conservative primary challenger. But after spending years deftly navigating his party and more than $10 million on his primary campaign, McConnell handily defeated Matt Bevin, 60 percent to 36 percent.

McConnell will now head into a showdown with Democrat Alison Lundergan Grimes, Kentucky’s secretary of state, in what could become the year’s most expensive Senate race.

In a preview of the vitriol to come, McConnell said in his victory speech Tuesday night that Grimes, whose father is a longtime Democratic official, is “a partisan’s partisan who’s been practicing party politics since she learned to talk.”

McConnell sought to connect her to Obama, saying, “Barack Obama’s candidates preach independence but they practice loyalty above all else. And tonight, I’m confident of this: Kentuckians will not be deceived. Alison Lundergan Grimes is Barack Obama’s candidate.”

Grimes came back fighting in her victory speech, delivering a litany of attacks on the Republican leader she labeled “Senator Gridlock.” She said she is “not an empty dress” and “not a rubber stamp,” but rather a “strong Kentucky woman” and an “independent thinker.”

“Mitch McConnell would have you believe that President Obama is on Kentucky’s 2014 election ballot,” Grimes said. “Senator McConnell, this race is between you and me.”

GOP hopeful in Ga., Ky.

In Georgia, where Democrat Nunn’s impressive early showing has turned the race for an open Senate seat into one of this year’s marquee contests, the most conservative tea party candidates struggled to catch on in a crowded seven-person GOP primary field.

The Republican race grew caustic in the closing days. Democratic officials said they hope the next two months prove tumultuous and damage the eventual nominee.

“This runoff is going to be an epic, nasty brawl,” said Matt Canter, deputy executive director of the Democratic Senatorial Campaign Committee. He said the primary campaign was “an out-of-control race to the fringe.”

In recent election cycles, Republicans nominated several flawed conservatives — including Sharron Angle in Nevada and Christine O’Donnell in Delaware in 2010, and Todd Akin in Missouri and Richard Mourdock in Indiana in 2012 — who made mistakes and lost races that Republicans were within reach of winning.

“If people were expecting history to repeat itself, where you have extreme and underfunded candidates get through — it doesn’t happen a lot,” said strategist J.B. Poersch, who ran the Democratic Senatorial Campaign Committee in its successful 2006, 2008 and 2010 cycles.

In all six states holding primaries on Tuesday, the differences between GOP candidates were more stylistic and rhetorical than ideological. The contrasts were not over policy and positions, but how they would legislate on Capitol Hill and how combative Republicans should be with Obama and Democratic lawmakers.

Tea party still optimistic

Leaders of conservative groups argued that this was evidence of establishment candidates adopting tea party principles, not of a diminished tea party movement.

“Everybody runs like a tea party candidate now,” said Matt Kibbe, president of FreedomWorks, a group that funds tea party activities. “Everybody is running against Obamacare and against overspending in Washington. It wasn’t always like that with the Republican establishment. I don’t even recognize McConnell from where he was a few years ago.”

Being prepared financially and politically to handle the volatility within the party’s base has been critical this year for Republican incumbents.

“No one is being caught flat-footed anymore,” said former congressman Steven C. LaTourette (R-Ohio), who heads the centrist Main Street Partnership. “The establishment is ponying up resources, and Republicans are generally starting to get behind some people who would like to see their government work. Tuesday should be a wake-up call to Democrats that Republicans are going to dig in and make a real play for the Senate majority.”

This looked to be the case from coast to coast. In Oregon, Monica Wehby, a well-funded pediatric neurosurgeon, won the Republican Senate nomination over her more conservative challengers, potentially putting the seat held by Sen. Jeff Merkley (D) in play.

A Boehner ally wins

In Idaho, home to one of the most hotly contested House Republican primaries, Rep. Mike Simpson beat Bryan Smith, who was backed by conservative organizations.

Simpson, an ally of House Speaker John A. Boehner (R-Ohio), came under attack for his vote for the 2008 bank bailout known as the Troubled Asset Relief Program. But with the support of the U.S. Chamber of Commerce and other mainstream GOP groups, he minimized Smith’s ascent.

Idaho Gov. C.L. “Butch” Otter was likely to defeat state Sen. Russ Fulcher in the GOP gubernatorial primary. The race gained notice from a colorful televised debate in which the two squared off, at times uncomfortably, against leather-clad motorcyclist Harley Brown and other political unknowns.

Tuesday’s Senate primaries in Arkansas were a mere formality, as Sen. Mark Pryor (D) and Rep. Tom Cotton (R) ran unopposed. The two have campaigned aggressively for months and their battle, in a state where Obama is deeply unpopular, is being closely watched. In the state’s gubernatorial race, Democrat Mike Ross and Republican Asa Hutchinson, both former congressmen, secured their nominations.

Earlier this year, GOP establishment favorites Rep. Shelley Moore Capito and state House Speaker Thom Tillis defeated more conservative challengers to win Senate nominations in West Virginia and North Carolina, respectively. Both seats are pick-up opportunities for Republicans. And in Texas, a bastion of tea party activism, Sen. John Cornyn defeated a group of primary challengers.

The trend could continue into next month. In South Carolina, Sen. Lindsey O. Graham is running ahead of his tea party opponents, as are Sens. Lamar Alexander (Tenn.) and Pat Roberts (Kan.). And in Iowa, state Sen. Joni Ernst and businessman Mark Jacobs, both favored by the GOP brass and business establishment, are outpacing contenders who claim to be purer conservatives.

The tea party’s only claim to statewide victory this year was in Nebraska, where Ben Sasse handily won the GOP Senate nomination last week. But although Sasse aligned himself with Sen. Ted Cruz (R-Tex.), he received significant support from Beltway officials. Sasse held several posts in the George W. Bush administration.

In Pennsylvania, much of the attention was on the Democratic side, where in the gubernatorial primary businessman Tom Wolf defeated Rep. Allyson Y. Schwartz, who had been the early favorite, and two other candidates. The winner will face Gov. Tom Corbett, a Republican considered perhaps the country’s most vulnerable governor.

With Schwartz vacating her suburban Philadelphia House seat to run for governor, the four-way Democratic primary to replace her carried national intrigue. Former congresswoman Marjorie Margolies, whose son is married to Chelsea Clinton, campaigned heavily on her Clinton connections, but she finished a distant second to state Rep. Brendan Boyle.