Chaffetz has said he will vote for GOP presumptive presidential nominee Donald Trump, but has also said he would use his chairmanship of the House Oversight Committee to watch and bridle some of Trump's wilder proposals.
Teng conceded at about 9:30 p.m.
"I knew it was a long shot, but I wanted to fix the way Utah's 3rd District is being represented. I knew that even if I didn't win, I could achieve some degree of change just by bringing certain things to light," he said in a statement.
Chaffetz, who is seeking a fifth term, and Teng, a Brigham Young University professor and former Microsoft engineer, waged a contentious campaign.
It even prompted Chaffetz to call Teng a "political hack" who spread misleading information, and said Teng is surrounded "by some goons that use old, tired tricks."
That came after Teng filed a complaint with the Federal Election Commission alleging that Chaffetz may be improperly benefiting personally from campaign donations — a charge Chaffetz denied.
Teng poured a half-million dollars of his own money into his campaign, 95 percent of the total he raised. "I'm not going out to ask for special-interest money, because they always come with strings attached," he said during the campaign.
Teng added that the $1 million that Chaffetz raised this cycle came largely from special interests. Chaffetz said his many donors show that he has broad support, and their money came with no strings.
Teng contended that Chaffetz has become part of the Washington establishment, and a change was needed to help balance budgets and stop tax hikes.
Chaffetz campaigned saying he has become a powerful voice for Utah in Washington. He used his chairmanship of the House Oversight Committee to bash Hillary Clinton over the terrorist attack on the U.S. embassy in Benghazi, rip federal funding for Planned Parenthood and push to impeach the IRS boss.
Chaffetz says he also pushes for government frugality, and he still saves money himself by sleeping on a cot in his office.
"I want to make people proud," he said earlier. "I want them to understand how hard I'm working to do the right thing."
Chaffetz will face Stephen P. Tryon in the November general election. Tryon ran as an independent in 2014 against Chaffetz, and won 1.8 percent of the vote. This time he is the Democratic nominee.