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.

Coming on the heels of Democratic triumphs in special elections for state legislative seats in Iowa and Pennsylvania and the defeat of four Republican-backed state referendums in Louisiana, Judge Crawford’s victory puts the party on its front foot for the first time since last November. Her win showed that, at least in one instance, Mr. Musk’s seemingly endless reserves of political cash had energized more Democrats than Republicans.

The race could also have implications for control of Congress, where Republicans’ razor-thin edge was fortified on Tuesday when the party held on to two Florida seats in special elections. Democrats have quietly argued for months that a Crawford victory would pave the way for a liberal-tilting Wisconsin Supreme Court to order new congressional maps, which could help Democrats defeat one or two of the state’s Republican Congress members.

Judge Crawford, of Dane County, herself participated in a meeting with liberal donors in January that was pitched as a chance to put two House seats in play, a prospect echoed last week by Representative Hakeem Jeffries of New York, the chamber’s Democratic leader. And Republicans, led by Mr. Musk, sought to make that possibility the central focus of their campaign to defeat her.

Mr. Musk, describing the stakes of the contest in near-apocalyptic terms, seemed to personify the campaign on Judge Schimel’s behalf even more than the candidate himself. Never before had a single donor sought to influence an American judicial race to such a degree, and few had invested comparable sums in an election in which they were not themselves running. Through his super PAC, Mr. Musk underwrote an $11.5 million ground game that targeted voters with messages urging them to help Mr. Trump by supporting Judge Schimel. A separate organization with Musk ties spent $7.7 million on television advertising, according to AdImpact, a media-tracking firm.

Mr. Musk also offered Wisconsinites $100 each to sign a petition in opposition to “activist judges.”

By Tuesday, his super PAC was offering voters $50 to post a picture of a Wisconsin resident outside a polling place.

The victory for Judge Crawford, 60, who won a 10-year term, maintains a 4-to-3 majority for liberals on the court, which in coming months is poised to deliver key decisions on abortion and labor rights. It may soon determine the legality of the state’s congressional district lines, which were drawn by the Republican-controlled State Legislature and have delivered six of eight House seats to the G.O.P. in the evenly divided state.

Liberals are likely to maintain a court majority until at least 2028. Conservative justices on the court face re-election in each of the next two years. Unless a liberal justice vacates her seat and is replaced by the governor, conservatives cannot flip a seat until 2028.

With control of the court on the line, the formally nonpartisan election was always going to be expensive and hard-fought, but Mr. Musk’s investment beginning in mid-February supercharged the stakes, attention and cash flowing into the state. The involvement of the billionaire, whose electric-vehicle company, Tesla, sued Wisconsin in January for the right to open dealerships in the state, turned what would have been a state contest into something approaching a national bat signal for Democrats to support Judge Crawford.

“This is a test, and the whole world is watching,” Ben Wikler, the chairman of the Democratic Party of Wisconsin, told supporters at Judge Crawford’s closing rally on Monday. “This is a chance for us to show that in a moment that is so terrifying nationally that we still believe in democracy.”

Backed by the Democratic Party of Wisconsin and the Democratic National Committee, and with visits from prominent liberals and Democrats including Gov. Tim Walz of Minnesota and Senators Bernie Sanders of Vermont and Amy Klobuchar of Minnesota, Judge Crawford raised $17 million in the fund-raising period ending March 17, a stunning figure for a state judicial candidate with little profile inside her state, let alone nationally.

Judge Schimel, 60, of Waukesha County, a longtime Trump loyalist who last year dressed up as Mr. Trump for Halloween, embraced the president and Mr. Musk with gusto in the campaign’s final weeks. He wore the president’s signature Make America Great Again hat to campaign stops and appeared with both Mr. Trump and Mr. Musk on livestreams in late March.

Wisconsin Republicans made no secret of their effort to make Judge Schimel, who served one term as the state’s attorney general before losing re-election in 2018, an avatar of the Trump movement. Brian Schimming, the Republican Party of Wisconsin chairman, said his goal was merely to get 60 percent of Mr. Trump’s voters from last November to turn out for Judge Schimel by Tuesday.

Judge Schimel, like Judge Crawford, framed the race as an existential threat to the state and the nation.

“If we don’t restore the court, our Republic will not survive, right?” he told supporters last week at a rally in Stoughton, Wis. “Frankly, they’re taking away one of the branches, right, by legislating from the bench.”

In Mr. Musk’s foray into campaigning on behalf of Judge Schimel, he made a show of his wealth but frequently digressed from the contest at hand.

On Sunday night, he traveled to Green Bay, where he came bearing a pair of $1 million checks to voters, winners, he said, of a contest among those who had signed his petition. One recipient just happened to be the chairman of the College Republicans of Wisconsin, who joined a third person to whom Mr. Musk’s super PAC had given a $1 million check a few days earlier.

But Mr. Musk spent just a couple of minutes out of his two hours of remarks addressing Judge Schimel and the coming election. In what came across as an unedited TED Talk, Mr. Musk delivered extended monologues about immigration policy, alleged fraud in the Social Security system and the future of artificial intelligence, in addition to taking a series of questions from the audience that also did not address the court race.

When Mr. Musk did address the reason for his visit, he framed the election in maximally important terms — suggesting Wisconsin voters were the first domino in a process that could change the future of civilization.

“What’s happening on Tuesday is a vote for which party controls the U.S. House of Representatives — that is why it is so significant,” Mr. Musk said. “And whichever party controls the House to a significant degree controls the country, which then steers the course of Western civilization. I feel like this is one of those things that may not seem that it’s going to affect the entire destiny of humanity, but I think it will.”

Wisconsin Democrats and others tied to Judge Crawford’s campaign found the whole episode confusing. Mr. Musk, while popular with conservative voters because of his ties to Mr. Trump, had not emphasized public safety or even affinity with the president — issues that Democrats believed had the potential to help Judge Schimel sway Republicans to vote.

Instead, they believed, it was the latest evidence that the one general-election candidate Mr. Trump can truly drive to victory is himself.

Jess Bidgood contributed reporting from Stoughton, Wis.