Mullins will face incumbent U.S. Rep. Ben Ray Luján, unopposed in the Democratic primary, in the Nov. 2 general election.
Mullins celebrated his victory at Courtyard by Marriott on Tuesday night.
"What's next is 153 days of campaigning in order to win back the seat for the people of New Mexico," Mullins said.
San Juan County voters overwhelmingly chose Mullins, who received more than 80 percent of the vote with 96 percent of precincts reporting in San Juan County.
"It was clear that he had the leadership of the party behind him," Kokesh said. "The Republican Party, the leadership is out of touch with it's own base. Our own leadership in our party is corrupt."
Luján, seeking re-election to a second term, said in a telephone interview from Santa Fe that he would continue to stand up to Wall Street, cut taxes for businesses and families, create jobs and take on credit card and health insurance companies.
"I share the frustration that many other New Mexicans do: that Washington is broken," he said. "People are tired of the fighting and the bickering, and we need to make sure that we're taking care of business and looking after them and putting people first."
Republican voters said they chose Mullins for his Farmington ties and support for the energy industry.
Neil Frost, a Farmington resident who works for an oil and gas company, has known Mullins for 10 years. The candidate will protect the Constitution and the oil and gas industry, Frost said.
"He's a swell guy," Frost said. "He's a good family man and he's done a lot for the industry."
Mullins and Kokesh battled throughout the district for the Republican nod, sharing similar views on some issues and differing on others.
Mullins, partial owner of oil and gas company Synergy Operating LLC, held strong views on energy policy.
"The most important issue facing our country right now is energy and we're seeing that in the Gulf of Mexico right now and also within the state's economy, which is so dependent upon oil and gas," Mullins said. "I think I bring the expertise and the knowledge to Washington that will benefit the people of New Mexico."
Kokesh held fervent beliefs on foreign affairs and veterans' health. He said better care was needed for veterans to reduce troop suicides.
Kokesh enlisted in the U.S. Marine Corps when he was 17 and went to Iraq in 2004, he said.
He believed the Iraq War was unconstitutional and that the government should reduce the number of troops in Afghanistan.
Mullins has said the government should bring troops home from the wars "as soon as possible, but we need to come home with victory."
The candidates also differed on congressional salaries.
Kokesh said he would have accepted only a $50,000 salary while Mullins favored reducing congressional pay by 25 percent and eliminating health care benefits.
Steve Lynn: email@example.com