Nebraska is a solidly Republican state, but Democrats think they have a shot of winning with Kerrey, a former senator, governor, and presidential candidate who easily won the Democratic nomination.
The general-election winner will replace Democratic Sen. Ben Nelson, who is not seeking a third term.
The GOP battle showed a split between the establishment Republicans, who favored State Attorney General Jon Bruning, and tea partyers, who helped Fischer make a late play for the nomination. State Treasurer Don Stenberg also was on the ballot for his fourth attempt to become a U.S. senator.
Elsewhere, Mitt Romney won the Oregon primary and was expected to win most or all of its 25 presidential delegates. Romney also won the Nebraska primary, but no delegates were allotted in a vote that amounted to a beauty contest. The state's 32 delegates to the Republican National Convention later this year will be determined at the state convention July 14.
Not counting Oregon's results, Romney was 171 delegates short of the 1,144 needed for the nomination and is on pace to get them before the month ends. He was spending the day in Iowa, a competitive general-election battleground, delivering a speech on the economy as he looks to counter President Obama on voters' top concern.
Romney painted Obama as a reckless steward of the country's economy and, as proof, pointed to "a financial crisis of debt and spending that threatens what it means to be an American."
"A prairie fire of debt is sweeping across Iowa and our nation, and every day we fail to act that fire gets closer to the homes and children we love," Romney told supporters at a downtown Des Moines hotel.
"This is not solely a Democrat or a Republican problem," Romney added. "The issue isn't who deserves the most blame; it's who is going to do what it takes to put out the fire."
The White House dismissed Romney's critique, blaming federal overspending primarily on Romney-backed tax cuts for the wealthy that were enacted during President George W. Bush's administration and on the wars in Iraq and Afghanistan.
The biggest race Tuesday was Nebraska's GOP Senate primary.
Democrat Nelson, a two-term moderate, is retiring, and both parties are eyeing his seat. Democrats want to keep it to maintain their Senate majority, while Republicans see an opportunity in their drive to win back control of the Senate.
Democrats control the Senate 51-47, plus two independents who caucus with the majority. But the outcome in November of several competitive Senate races could result in a power shift.
Republicans in Washington turned to Bruning, who had been successful in statewide races. But in the final stretch of the Senate campaign, he found that his nomination was hardly assured as Fischer, a rancher in rural Nebraska, mounted a late run to win.