"It is the time for a new generation of leaders. We know it to our bones," said Liljenquist, 37. "We have two more months. We feel good about our chances."
Hatch will begin the next phase with the momentum from convention and far more financial support, but it's not unheard of for a newcomer to topple an incumbent in a primary. Jason Chaffetz beat Rep. Chris Cannon in 2008.
The senator says he's confident he will come out ahead this time.
"We're going to win it," he said, calling the vote "a tremendous victory" even if he didn't win the nomination outright.
"We're pretty darn happy about what did happen. It sent a message. It says that this tough old bird isn't someone you can just trample on."
The race has received widespread national attention, with tea party groups such as FreedomWorks targeting Hatch and spending more than $700,000 in a campaign to defeat him and boost Liljenquist.
The senator has spent millions of dollars and amassed a campaign staff of more than two dozen to recruit delegates and fight the tea party wave that consumed former Sen. Bob Bennett at the state convention two years ago.
So far, the race has hinged on Hatch's longevity. The senator touts his seniority on the Senate Finance Committee, which he may lead if Republicans take control of the Senate after the 2012 election.
Liljenquist's slogan has been "It's time," a not-too-subtle jab at Hatch's lengthy tenure in Washington, which he argued was dotted with votes to expand the role of government and add to the national debt.
Both candidates hit these familiar notes when addressing the nearly 4,000 delegates on Saturday.
With a feisty demeanor and a hoarse voice, Hatch called himself "a tough old bird" and promised that this would be his last election.
"It will be my last six years in the U.S. Senate," he said. "But they'll be the best six years and the most critical six years of all."
Hatch also had a video message from Mitt Romney, who apologized for not attending in person.
"We need Orrin Hatch back in the Senate helping to lead the way," Romney said.
Hatch argued that he was the only candidate with the clout to fight for control of Utah's federal lands or protect Hill Air Force Base.
He didn't reference his challengers. Liljenquist, by contrast, took direct aim at Hatch, arguing: "No senator is king, no matter what seat he is in."
He promised that he wouldn't move to Washington, would support term limits and would try to eliminate congressional pensions. He ended his speech by mentioning the plane crash he survived before getting involved in politics.
"It stamped on my mind a sense of urgency I did not feel before, but I feel now," he said.
Thomas Burr contributed to this report.