WASHINGTON (CNN) -- -

Tuesday's Senate primary in Kansas ended another ugly showdown that pit a tea party-backed challenger against an establishment Republican incumbent.

CNN projects incumbent Sen. Pat Roberts has fended off conservative challenger Milton Wolf in the state's GOP Senate primary.

In his victory speech Roberts said that "we celebrate tonight" and that "we have another job starting first thing tomorrow."

"That job is to unite Republicans under a common and vital cause," he said. "Unity must happen if we are to keep Kansas red. It must happen if we are going to defeat an Obama agenda and send Harry Reid back!"

The race saw controversies over residency and Facebook photos and a rare streetside confrontation.

Roberts' win leaves only Thursday's nominating contest in Tennessee, where incumbent Lamar Alexander faces a bunch of conservative challengers, for a tea party-backed candidate to prevail in Senate primaries.

Wolf's campaign for months tried to portray Roberts as more in tune with Washington than Kansas, pointing to reports from earlier this year that the senator listed his voting address at the home of two longtime political supporters who rent a room to him.

Wolf said in his concession speech that "while we came up short tonight, I believe our battle just begins."

"I believe we're just getting warmed up," he said to his supporters.

"I believe we're going to save this country because it's up to us. Our republic needs us to stand up and fight and it is the greatest honor of my life to stand shoulder to shoulder with you," he said. "To run towards the screaming instead of away. And I will always stand up and fight for our country and fight for our state. And it is the biggest honor of my life to say that I stood with you."

Still, Roberts was seen as the heavy favorite in the nomination battle with a large double-digit lead in the most recent poll. A couple of other minor candidates were also on the ballot.

Dueling controversies

The Wolf campaign ran numerous ads attacking Roberts over his residency.

At the same time, the Roberts' campaign over the past couple of months went up with TV ads reminding voters that Wolf, a radiologist, posted X-ray images of mortal injuries and made light of them and the victims. Wolf was later forced to admit he made "insensitive" comments.

Wolf painted himself as a conservative activist with the guts to stand up to the GOP establishment.

As a doctor, he frequently campaigned against the Affordable Care Act and proposed his own plan that he calls "PatientCare."

He enjoyed the backing and the support of some major national tea party groups, such as the Tea Party Patriots and the Tea Party Express, and some influential anti-establishment organizations, like the Senate Conservatives Fund and the Madison Project.

Roberts enjoyed the support of the National Republican Senatorial Campaign, which is chaired by fellow Kansas Republican Sen. Jerry Moran.

Showdown on the street

In the closing weeks of the primary campaign, Wolf highlighted what he said was Robert's refusal to debate him. Last week, Wolf changed his travel plans at the last minute to confront Roberts as he met with business leaders in Emporia, Kansas.

"You told Kansans you would give them your word and you would give them a debate," Wolf said to Roberts.

"You have said it multiple times in multiple places. You tell us that you are tough and you're tested and trusted. And I want you to keep your word on that, I want you to debate. I think Kansans deserve it."

"Milton, Milton, Milton, Milton," Roberts said dismissively. "This is not the time. We have a regularly-scheduled event, a listening tour event. This is not the time."

"When would be the time, senator, because I'll go anywhere you'd like. You've given your word to debate. Let's just debate," Wolf continued as Roberts walked off.

Roberts' campaign was asked why he wouldn't debate.