With about one-fourth of the votes counted, the 78-year-old Hatch led by a wide margin, The Salt Lake Tribune reported.
The battle between Hatch and state Sen. Dan Liljenquist, 37, was another contest between an elected official and those who want to cleanse the GOP of opponents to Tea Party principles, CBS News reported.
Hatch's most vocal critic has been Tea Party supporter Freedom Works, headed by former House Majority Leader Dick Armey, R-Texas. While Liljenquist has raised about a half million dollars, the group has spent $945,000 on television advertising, phone calls and direct mail advertising to defeat Hatch.
Hatch has spent $9.8 million to hold onto his Senate seat, the most recent Federal Election Commission filing indicates.
Hatch called Freedom Works "the sleaziest bunch I've ever seen in my life" in a radio debate.
The group has been a key player in the recent defeats of Republican Sens. Bob Bennett of Utah in 2010 and Richard Lugar of Indiana this year.
A Deseret News/KSL-TV poll conducted June 15-21 indicated 60 percent of Utah's registered Republican voters planned to go for Hatch and 32 percent backed Liljenquist. The poll has a margin of error of plus or minus 3.6 percentage points.
"Those are very good numbers for the senator," Hatch campaign manager Dave Hansen told the Deseret News.
Liljenquist said his "biggest challenge by far is name recognition."
"We're going after a guy who has perfect name recognition in this state and has reinforced it with $10 million of spending and big endorsements," he said.
Hatch -- whose campaign said it benefited greatly by the endorsement of presumptive GOP presidential nominee Mitt Romney -- will face Democratic nominee Scott Howell in the general election. Hatch beat Howell in the 2000 election.