With 75 percent of precincts reporting, Fisher led Secretary of State Jennifer Brunner 54 percent to 46 percent, prompting Brunner to concede.
In a concession statement, WTTE-TV in Columbus reported Brunner congratulated Fisher and said she is "looking forward to a vigorous campaign in the fall" as the Democrats try to wrest the Senate seat from the Republicans with the departure of GOP stalwart Voinovich. Portman is a former congressman.
In addition, voters will choose Republican and Democratic nominees for the state's representation in the U.S. House.
In Ohio's 17th Congressional District GOP primary, pharmacy services manager Jim Graham defeated Dr. Murrell "Bing" Henderson. He and convicted former Congressman James Traficant Jr., who is running as an Independent, will face Democratic incumbent Tim Ryan in the general election in November.
Ohio voters also were approving a measure to borrow $700 million for five years to help high-tech businesses.