Steve Hilton, a Republican, and Xavier Becerra, a Democrat, were leading in election night returns. Tom Steyer, another Democrat, urged patience as more votes were being counted.
Without a dominant candidate in the governor's race, Democratic voters ultimately wanted to ensure that their party wasn't shut out of the general election.
Ms. von Wilpert's win in Tuesday's open primary eliminated Democrats' fears that two Republicans would advance to November in the 48th Congressional District.
Businessman Zach Lahn addressed his supporters following the concession by Rep. Randy Feenstra, a Trump-backed candidate, in the Republican primary for Iowa governor. Lahn will face Democrat Rob Sand in the November general election.
The president's pick for governor of Iowa lost his primary, while Democrats in the state chose their nominee in what they hope will be a competitive Senate race.