With 76 percent of precincts reporting, Vance has 31.4 percent of the vote, followed by Josh Mandel with 24.3 percent and Matt Dolan with 22 percent. Vance received the endorsement of former President Donald Trump last month.
In November, Vance will face off against Rep. Tim Ryan (D-Ohio), the clear winner of the Democratic Senate primary. They are vying to take over the seat being vacated by retiring Sen. Rob Portman (R).
In other Ohio primary news, Gov. Mike DeWine (R) won the GOP nomination for a second term, with Nan Whaley, the former mayor of Dayton, winning the Democratic nomination.