A liberal candidate for a pivotal seat on the Wisconsin Supreme Court overcame $25 million in spending from Elon Musk and defeated her conservative opponent on Tuesday, The Associated Press reported, in a contest that became a kind of referendum on Mr. Musk and his slashing of the federal government.

With turnout extraordinarily high for a spring election in an off year, Judge Susan Crawford handily beat Judge Brad Schimel, who ran on his loyalty to President Trump and was aided by Mr. Musk, the president’s billionaire policy aide.

Mr. Musk not only poured money into the race but also campaigned personally in the state, even donning a cheesehead. But his starring role seemed to inflame Democratic anger against him even more than it helped Judge Schimel.

The barrage of spending in the race may nearly double the previous record for a single judicial election. With about 95 percent of the vote counted on Tuesday evening, Judge Crawford held a lead of roughly 9 points.

“Today, Wisconsinites fended off an unprecedented attack on our democracy, our fair elections and our Supreme Court,” she said in her victory speech on Tuesday night. “Wisconsin stood up and said loudly that justice does not have a price. Our courts are not for sale.”

For Democrats, the result is a jolt of momentum. They have been engaged in a coast-to-coast rhetorical rending of garments since Mr. Trump returned to the White House in January and embarked with Mr. Musk on an effort to drastically shrink federal agencies, set aside international alliances and alter the government’s relationships with the nation’s universities, minority groups, immigrants and corporate world.

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