The vote was overwhelming in Sharer's favor. Sharer had captured 70.8 percent of the vote, with 11,154 votes to 4,601 for Dodson, according to unofficial results from the San Juan County Clerk's Office.
Sharer, a veteran who served in the U.S. Army Rangers, was first elected to the state Senate in 2000.
"I think part of me still has the obligation to serve," he said. "Certainly being in the minority in the New Mexico Senate, you have to fight hard. Some of that's still in my system and I can't get it out."
Sharer said his constituents' strong support helps him take unpopular stands in the Senate. "That's put me in a position where I can fight some of those fights," he said.
Sharer, 53, owns and operates CBF Services, a Farmington business founded in 1948 and formerly owned by his father. The business collects debts, sells credit reports and teaches a financial literacy course.
Dodson, 48, faced an uphill battle against the incumbent in Senate District 1, home to more than 13,000 registered Republicans and about 7,000 Democrats. The staunchly conservative district encompasses downtown Farmington.
He conceded defeat Tuesday night.
"I call that definitive," Dodson said. "Clearly I got beat."
Dodson held out the possibility of running again.
Sharer ran unopposed in 2008.
Sharer said he is likely to continue serving on the Corporations and Transportation Committee. When he returns to the Roundhouse in Santa Fe, Sharer wants to simplify New Mexico's tax code for businesses.
"When businesses are looking at coming here, they just look at it and say, This is too hard, we're gone,'" he said. The tax code should be changed "so that businesses understand it."
Sharer is married to Beth, and they have two adult children. Their son, Sean, works at CBF Services, and their daughter lives in Washington state.
Dodson spent part of Tuesday replacing campaign signs that were apparently removed. "Some were consistently taken," he said. "But a lot of them weren't."
A U.S. Air Force veteran who has lived in Farmington for more than 20 years, Dodson ran on a platform of reducing inequality, expanding health care and improving public infrastructure. His wife, Maria, works at San Juan College.
Sharer attracted far more donations than his challenger. Sharer raised $47,576 and spent $35,416 as of Oct. 30, according to the New Mexico Secretary of State's office. Dodson raised $4,330 and spent $3,381 as of Oct. 31.
Pat Cordell, chairman of the San Juan County Republican Party, said Sharer is a good fit for his constituents.
"He tells it like it is," Cordell said. "He's very conservative, and fiscally conservative, also. I think they just like the job he's done."