The former senator was projected to take 92.5% with 1% counted, setting up a November special-election contest with Republican incumbent Jon Husted for the final two years of JD Vance's term.
The race is a key test of Democrats' chances of cutting Republicans' 53-47 Senate majority in a state that has trended Republican but is now seen by some analysts as competitive.
Turnout and other Ohio contests, including House races involving Marcy Kaptur, Greg Landsman and Emilia Sykes, are also being watched for clues about Democratic strength in the midterms.
How could Ohio's special election results potentially reshape the current majority in the U.S. Senate?
Whose economic vision will ultimately win over Ohio voters in this closely contested Senate election?
With record outside spending in Ohio, can grassroots fundraising still compete in a pivotal Senate race?