Roberts overcame questions about his Washington-area home, his Kansas rental for official residency and his quip that he goes home when he gets an opponent.
"My posse did not flinch, even though there were times when their candidate — me — stepped on our message," he said.
The Senate GOP establishment, burned in 2010 and 2012 when tea partyers and outsiders cost them majority control, is now basking in a solid string of wins — Texas, Kentucky, South Carolina and Mississippi, though it took six-term Sen. Thad Cochran two tries there before defeating Chris McDaniel, who is challenging the outcome.
Establishment Republicans are upbeat about Thursday's primary in Tennessee, where they expect two-term Sen. Lamar Alexander to turn back a challenge from state Rep. Joe Carr.
Three months to Election Day, the GOP is increasingly optimistic about gaining the six seats necessary to seize control of the Senate, no longer worried that not-ready-for-prime-time candidates will stumble in the general election.
While Roberts prevailed, a House incumbent lost in his re-election bid.
Businessman and lawyer Dave Trott easily defeated Rep. Kerry Bentivolio, 66 to 34 percent, in Michigan's 11th Congressional District, a reversal of the recent political order of tea partyers targeting an establishment favorite.
Bentivolio, a part-time reindeer rancher, was often described as the "accidental" congressman, as he was elected in 2012 when former Rep. Thaddeus McCotter turned in fraudulent voter signatures for a ballot spot. Bentivolio became the third House incumbent to lose in the primary, joining Republican Reps. Eric Cantor of Virginia, the former majority leader, and Ralph Hall of Texas on the House casualty list.
He was unapologetic in defeat, railing against "crony capitalists."
"The status quo in the Republican Party is going to have to change whether they like it or not," Bentivolio said in his concession speech. "They will no longer be allowed to have our vote simply because we dislike the Democrats more."
Another Michigan Republican, tea party favorite and two-term Rep. Justin Amash, turned back a challenge from businessman Brian Ellis.
Primaries on Tuesday in Kansas, Michigan, Missouri and Washington state launched a crowded stretch that continues with Tennessee on Thursday, Hawaii on Saturday and Connecticut, Minnesota and Wisconsin next week. By month's end, voters will decide the Republican Senate nominee in a competitive race against Sen. Mark Begich in Alaska and the Democratic primary between Hawaii Sen. Brian Schatz and Rep. Colleen Hanabusa.
The 78-year-old Roberts, a conservative, moved even farther right as he faced a tough re-election. The senator, who backed the nomination of former Gov. Kathleen Sebelius to be secretary of Health and Human Services, was one of the first to call for her resignation after the disastrous launch of the health care website last October. Roberts also voted against a U.N. treaty on the rights of the disabled in December 2012 despite the appeals of former Kansas Sen. Bob Dole, who sat in a wheelchair in the well of the Senate.
Wolf argued that Roberts had spent too much time in Washington and came up short as a true conservative. Wolf eagerly disavowed the policies of his cousin Obama, especially on health care, and had the backing of the Senate Conservatives Fund and several tea party groups.
But Wolf was dogged by X-rays of gunshot victims that he posted on a Facebook page with humorous comments. Wolf acknowledged the mistake and apologized, but Roberts made it an issue in campaign ads.
Roberts will face Democrat Chad Taylor in November in the solidly Republican state.
In Washington state, former Washington Redskins football player Clint Didier advanced to a Republican-versus-Republican general election matchup against Dan Newhouse for the seat of Rep. Doc Hastings, who is retiring after 10 terms.