Nielsen won narrowly in Elmore County 1100-1046, lost to Millington 258-437 in Twin Falls County, and carried Owyhee County by a 690-482 margin, for a total victory of 2,048-1,965 (51 percent).
Incumbent GOP legislators Rich Wills (House seat A) and Sen. Bert Brackett were unopposed on the ballot. Wills received 1,880 votes. Brackett earned 1,835.
On the Democratic ballot, Mary Ann Richards, who will face Wills in the fall, received 256 votes, while Spike Ericson, who will challenge Nielsen, received 234 votes.
Voters in the Glenns Ferry School District rejected a $500,000 per year supplemental levy by a 296-260 margin.
The Bruneau-Grand View School District's second request this year for a $600,000 supplemental levy failed, losing 261-249 in Owyhee County, even though Elmore County's share of voters said yes by a 34-16 margin.
Those were the only supplemental levy requests in the state to go down to defeat. The seven others being sought all passed.
In the race for county commissioner from District 1, first-term incumbent Bud Corbus easily turned back a challenge by Courtney Ireland 1,394-770.
The District 2 county commissioner seat was a three-way race between incumbent Wes Wootan, who garnered 991 votes to win re-election to a second term, Doug King, who earned 488 votes, and Robbin Ellis, who received 650 votes.
None of the other local GOP races saw any challenges. Nevertheless, Assessor Ron Fisher received 1,931 votes, County Clerk Barbara Steele earned 1,926 votes, Amber Sloan, the designated successor to retiring Treasurer Rose Plymton, garnered 1,879 votes and County Coroner Jerry Rost received 2,039 votes.
No other local candidates were listed on the Democratic ballot.
Tuesday's primary election was one of the lightest turnouts in years, both locally and statewide. In Elmore County only 28 percent of registered voters cast ballots and only 17 percent in Twin Falls County.
The key races were on the Republican ballot, since very few Democrats were expected to have any serious chance in the November elections for state and national elections -- and Elmore County elections as well.
In the hotly contested GOP precinct committeemen race, where moderates were trying to regain control of the Elmore County Central Committee from Tea Party supporters, state GOP chairman Barry Peterson turned back a challenge from former state senator Tim Corder 150-130 in Mountain Home precinct #8, but, in general, the moderates were taking most of the contested positions.
In the bitter race between incumbent Jace Prow and challenger Geoff Schroeder in Mountain Home #4, Schroeder held a narrow 87-82 lead in unofficial returns.
In the other contested GOP committeeman races, Mark Bryant edged John Barrutia 82-72 in Mountain Home #2, Rich Sykes rolled past Larry Heinen in Mountain Home #6 by a 110-60 margin, Arlie Shaw defeated Larry Jewett 128-68 in Mountain Home #7, Bud Corbus rolled past Christopher Pentico 123-60 in Mountain Home #9, Christy Zito slipped past Megan Blanksma 44-36 in the Hammett precinct, Judith Lords held a slim 7-6 lead in unofficial returns in the Atlanta precinct, and Monty White defeated Dewey Crane 133-104 in the Glenns Ferry precinct.
All the other precinct races were unopposed. In Mountain Home #1 Ray Liercke received 69 votes, Fred Perez received 151 in Mountain Home #3, Sumner Price garnered 129 votes in Mountain Home #5, E. Bunni Barnhame got five votes in the Camas Precinct and Donna Bennet got 23 in Chatten Flats, John Walker received 70 votes in the King Hill precinct, Jolene Hobdey got 30 in the Mayfield precinct, Gary Freeman received 35 in Pine and Mary Cook earned 19 in the Prarie precinct.
On the Democratic side, precinct committeemen were put forward in only five of the 18 precincts, and all ran unopposed. Nancy Orr received 43 votes in the Glenns Ferry precinct, Spike Ericson earned three in the Mayfield precinct, Joyce Allgood earned 26 in Mountain Home #1, E. Gaylene Gries receivd 22 in Mountain Home #3 and Aaron THomas earned 21 votes in Mountain Home #7.
In some of the more prominent statewide races on the GOP ballot, Elmore County voters:
* Preferred local candidate for state Superintendent of Public Instruction Sherri Ybarra, earned 1,190 votes over challengers Jon Eynon (237), Andrew Grover (311) and Randy Jensen (328). Unofficial statewide returns had Ybarra leading with 28.4 percent of the vote. Randy Jensen was in second place with 24.3 percent.
* In the race that was being watched with national implications, incumbent Second District Congressman Mike Simpson won locally by a 1,476-740 margin, and statewide held a 61.6 percent lead Wednesday morning over challenger Bryan Smith.
* For governor, incumbent Butch Otter received overwhelming approval locally, earning 1,404 votes to Russell Fulcher's 681, Harly Brown's 92 and Walt Bayes' 49.
For state and national races, both parties had challenged positions. The following results are for Elmore County only.
On the Republican ballot:
* Incumbent U.S. Senator Jim Risch defeated Jeremy Anderson 1,671-503.
* For lieutenant governor, incumbent Brad Little earned 1,656 votes to Jim Chmelik's 476.
* For Secretary of State Lawerence Denney received 578 votes, Mitch Toryanski had 312 votes, Evan Frasure got 280 votes locally and Phil McGrane received 790..
* For state controller, incumbent Brandon Woolf received 1,103 votes to Todd Hatfield's 869.
* For attorney general, incumbent Lawrence Wasden received 1,300 votes while challenger "Chris" Troupis earned 724.
On the Democratic ballot at the state and national level, votes in Elmore County were cast for:
* United States senator, where Nels Mitchell received 177 votes to 83 votes for William Bryk (who lives in Brooklyn, N.Y., and also was running for senate positions in Oregon and Alaska).
* For governor, A.J. Balukoff received 141 votes locally to Terry Kerr's 125.
* State treasurer, where W. Lane Startin earned 45 votes to Deborah Silver's 208.
Running unopposed on the Democratic ballot were: Richard Stallings, who received 256 votes in his bid to challenge Simpson this fall for the Second Congressional seat; lieutenant governor candidate Bert Marley received 244 votes; Jana Jones, making her second bid for Superintendent of Public Instruction, received 261 votes; Secretary of State candidate Holli Woodings garnered 251 votes, and attorney general candidate Bruce Bistline received 241 votes.
There are no other challenges on the Democratic ballot and many positions had no candidates at all.
In the non-partisan ballots for various judge positions, incumbent state supreme court justice Joel Horton received 1,494 votes to 779 votes foor his challenger, William Seiniger.
Unopposed on the ballot were Supreme Court Justice Warren Jones, who received 2,065 votes, and appeals court judged Sergio Gutierrez, who received 2,067 votes.
In the race for Fourth District Court judge, where the position of retiring judge Mike Wetherell was being sought by four challengers, Rebecca Arnold (549 votes), Samuel Hoagland (1,073 votes), Jeanne Howe (311 votes) and Jonathan Medema (357 votes).
The other challenged Fourth District judge race saw Richard Greenwood receive 1,339 votes locally to Les Bock's 937.
Fourth District Court judges who were unopposed for election were: Deborah Bail (2,106 votes), Cheri Copsey (2,075 votes), Timothy Hansen (2,052 votes), Melissa Moody (2,061 votes), Thomas Neville (2,052 votes), Lynn Norton (2,053 votes), and Patrick Owen (2,041 votes).