Republican Ruth McClung and Libertarian George Keane will move on to compete for U.S. Rep. Raúl Grijalva's seat in the general election for the U.S. House in Southern Arizona's District 7.
McClung was emerging from a five-way Republican field with more than half of the votes cast in the race early in the evening.
Her top concern is reining in Washington's spending, and she has said the immigration and border issues must be solved because of the financial cost and human impact of people dying in the desert.
The 28-year-old rocket scientist said her background would help her deal with some of Congress' complex problems.
Her closest competitor, Terry Myers, was hovering at just over 22 percent of the ballots counted late in the evening. The 58-year-old development-services consultant said his business experience set him apart from the other candidates. He said he was "answering a call" to run for office and see if his ideas resonated with voters. His top priority was jobs.
Christopher Flowers, Joseph Sweeney and Robert Wilson also competed in the Republican primary.
Keane defeated Andrew Ibarra for the Libertarian nomination with about 55 percent of the votes counted by late Tuesday evening.
Both candidates had only recently changed their voter registration to Libertarian.
Keane, a 32-year-old loan servicer for a mortgage company, said he was disenchanted with the Republican Party. He said Americans are "overtaxed and over-regulated." Among other priorities, he wants to get troops out of Afghanistan to save money and lives, and he opposes Grijalva's vote to pass the health-care law.
Ibarra, 55, is a controller for a tire company. He has said he's concerned about the economy.
An independent committee hoping to get more conservative congressional representation spent money in the Republican primary. Conservatives for Congress urged voters not to nominate Sweeney because the committee said he would embarrass the party if he were to compete in the general election. He has run for office several times before.
The winners will face incumbent Grijalva and independent Harley Meyer in November.
Grijalva holds an advantage in the district, where voter registration leans heavily Democratic, but he has been the subject of several protests due to his call for organizations to boycott the state after the governor signed the controversial immigration-enforcement measure into law last spring. He has since rescinded that call.
Contact reporter Andrea Kelly at firstname.lastname@example.org or 807-7790.