By David Schwartz

PHOENIX (Reuters) - Conservative Arizona congressman Jeff Flake is favored to defeat a feisty political newcomer with deep pockets in a primary election on Tuesday for a Senate seat that Republicans need to take the majority from Democrats in the November election.

Arizona's Republican Senate contest is the highest profile race among the primaries on Tuesday that also include votes in the states of Vermont and Alaska, as well as a runoff election in Oklahoma.

Flake, a six-term member of the House of Representatives, faces businessman Wil Cardon, a hard-liner on immigration who oversees his family's portfolio of real estate investments.

The winner will be the Republican nominee in the November election to replace Arizona Senator Jon Kyl, a Republican leader in the U.S. Senate who announced in February he would not seek a fourth six-year term in office.

The Democratic nominee in the November 6 general election is former U.S. Surgeon General Richard Carmona.

Both Kyl and Arizona Senator John McCain have endorsed Flake in a race that started out fiery but has cooled lately.

Cardon came out swinging early with a costly advertising blitz casting Flake as a Washington insider who favored tax increases and was soft on illegal immigration, although the challenger has reined in his spending in recent weeks.

"There is no reasonable explanation for stopping the spending other than they probably don't want to throw away any more money," said Jennifer Duffy, a senior editor at the Cook Political Report in Washington, D.C. "It says that Flake has a fairly healthy lead and Cardon's people can't find a way to diminish it."

RUNNING ON RECORD

Flake, 49, has focused the race on what he said is a "proven track record" of voting to reduce the size of government and cutting taxes and spending.

"People have seen what I've done already and they recognize the name and my record," Flake said in an interview between campaign stops in Yuma, Arizona. "These are things people agree with philosophically and they want that kind of activity in the Senate."

Promoted as a "battle-tested conservative," the former head of the Goldwater Institute in Arizona, which is named after longtime Arizona Senator and former Republican presidential candidate Barry Goldwater, has the support and funding of the Club for Growth business group and some Tea Party faithful.

Cardon, 41, has contributed nearly $8.8 million of his own money through the August 8 candidate filing period trying to establish himself as an outsider and businessman with experience.

"When you're running against the establishment you have to be able to put your own money into the campaign," said Cardon, following a panel discussion in southern Arizona.

Cardon is one of several self-financed business candidates running against established Republicans in Senate primaries this year. Businessmen lost in Missouri, Wisconsin and Michigan but former World Wrestling Entertainment chief executive Linda McMahon won the Republican nomination in Connecticut.

There has been a dearth of recent polls on the Arizona race. One in May by a Democratic polling firm had Flake's lead over Cardon at 22 points and another financed by a pro-Flake Republican group had the lead unchanged in late July.

Republicans already have a majority in the U.S. House and need to hold onto open seats such as Arizona and make a net gain of four in other states in order to take a majority in the Senate and control the policy agenda.

In another hotly contested Arizona primary race, two Republican incumbents will battle for the chance to make it to the November ballot for a House of Representatives seat.

Ben Quayle, son of former vice president Dan Quayle, takes on David Schweikert, in an expected tight contest brought about by the once-a-decade redistricting. It is one of 11 such House contests between incumbents nationwide this year.

(Editing by Tim Gaynor, Greg McCune and Bill Trott)