How Ted Cruz won the Wisconsin GOP primary, in 60 seconds (Peter Stevenson/The Washington Post)

Ted Cruz rolled to a landslide victory Tuesday in Wisconsin’s hotly contested Republican presidential primary, capitalizing on a difficult stretch for Donald Trump to cut into the front-runner’s overall delegate lead and deliver a psychological blow to the billionaire mogul.

Though the senator from Texas is reviled by many party leaders for his explosive and polarizing brand of politics, Cruz won over establishment Republicans as well as grass-roots conservative activists across this state who had come together in an urgent push to stop Trump. Late returns showed him leading Trump by a wide margin.

Cruz hopes his Wisconsin win transforms the trajectory of the race. Wisconsin adds a important Midwestern bellwether to the basket of mostly Southern or rural states he has won to date, giving the Texan evidence that he can appeal beyond ultra-conservative and religious voters.

Savoring his biggest night since winning the kickoff Iowa caucuses in February, Cruz declared before cheering supporters here in Milwaukee: “Tonight is a turning point. It is a rallying cry. It is a call from the hardworking men and women of Wisconsin to the people of America: We have a choice — a real choice.”

Trump remains in a favorable position nationally, but Cruz now has fresh momentum heading into future contests and Tuesday’s results increase the possibility that the nomination battle spills onto the floor of the party’s July convention in Cleveland.

Only 42 delegates were at stake in Wisconsin, however, meaning Tuesday’s primary will not significantly alter the delegate count, in which Cruz had been trailing Trump by roughly 250. To secure the nomination, candidates need 1,237 delegates.

“Either before Cleveland or at the convention in Cleveland, together we will win a majority of the delegates — and together, we will beat Hillary Clinton in November,” Cruz told supporters.

Trump spent the evening with his family in New York monitoring the returns and made no public appearance. His campaign issued a statement that read, in part: “Ted Cruz is worse than a puppet — he is a Trojan horse, being used by the party bosses attempting to steal the nomination from Mr. Trump. We have total confidence that Mr. Trump will go on to win in New York, where he holds a substantial lead in all the polls, and beyond.”

Trump is planning a large rally Wednesday night on Long Island and a visit to California later in the week.

Ohio Gov. John Kasich, who has been fending off calls from Cruz and Trump to quit the race, finished a distant third. He now looks to the April 19 primary in New York and contests later this month in Maryland, Pennsylvania and other states along the East Coast.

Kasich’s chief strategist, John Weaver, wrote a memo distributed Tuesday night that predicts a contested convention. “Tonight’s results will solidify the fact that no candidate will reach Cleveland with 1,237 bound delegates,” Weaver wrote.

Cruz used his victory speech to draw unmistakable contrasts with Trump’s incendiary campaigning. “We are not here to curse the darkness, but to light the candle that can guide us. . .to a safe and sane future,” he said. Then Cruz brought his wife, Heidi, the subject of a nasty feud with Trump and his fans, to the podium and showered praise on her.

For Trump, the loss here in a state where he had campaigned vigorously and which he vowed to carry caps a bruising few weeks. Since a March 15 romp in Florida and other states that seemed to position him as nearly unstoppable, Trump suffered a series of self-inflicted wounds from which he is struggling to recover.

In Wisconsin, Trump ran into a wall of hostility from influential conservative talk radio personalities as well as from Gov. Scott Walker and his loyal coalition of party activists, who had lined up behind Cruz.

Nearly half of voters in the GOP primary were looking for a president with experience in politics, according to preliminary exit-poll results reported by ABC News. That is an increase from earlier states that have voted, where only about four in 10 Republicans looked for someone with experience. Of those, just 7 percent backed Trump.

Trump’s previous wins have been fueled in part by voters who support his hard-line immigration position. But the exit polls show that in Wisconsin more than six in 10 Republican primary voters think undocumented immigrants should be offered a path to legal status — one of the highest of any state voting this year, according to ABC.

In the closing days of the Wisconsin race, Trump burrowed in to try to close a polling deficit with Cruz. He staged a series of relatively intimate rallies and town hall meetings and popped into diners to greet locals.

Trump played up his opposition to trade deals, which he thought would resonate with Wisconsin’s blue-collar voters — just as it had last month in neighboring Michigan, whose primary he won convincingly. And he was characteristically relentless in his criticism of Cruz and his allies, calling the senator “Lyin’ Ted” and belittling Walker by imitating him riding a Harley-Davidson motorcycle.

Trump also deployed his wife, Melania, to make a rare campaign appearance Monday night in Milwaukee — a move seemingly orchestrated to soften his image with women after a series of misstatements on abortion policy.

But it was not enough. In the exit polls, fully 35 percent of Republican primary voters said they would feel “scared” if Trump became president and another 20 percent expressed concern. Just over half singled out Trump for running the most unfair campaign and over one-third said they would not support him in a hypothetical general election.

Sensing a big win within his reach, Cruz spent the past week barnstorming the state with a caravan of well-known Republican supporters. They framed the primary as a pivotal moment in the push to deny Trump the party’s nomination.

Walker, himself a candidate before dropping out last fall, was a constant presence at Cruz’s side during the final 48 hours. The governor built intense loyalty from Republican voters here through his battles with the legislature and organized labor, including a brutal recall campaign in 2012 and reelection in 2014.

Walker tried to bestow his supporters to Cruz, introducing the Texan at large gatherings in Green Bay and Waukesha. Together they visited a touristy cheese shop in Kenosha, where Cruz sampled local cheddar, and posed for selfies at an Italian market in Milwaukee as Cruz and his family ate gelato.

Introducing Cruz on Tuesday night, Walker said, “This victory is bigger than just Wisconsin. This is the night when we can look back and say that was the time that turned the tide in this election.”

As Trump struggled for several days to explain his position on abortion, Cruz spotlighted his wife Heidi and former candidate Carly Fiorina to help make his soft pitch to women voters. Heidi Cruz and Fiorina staged their own series of meet-and-greets across the state.

Rolling across the state in his campaign bus through chilly weather and the occasional dusting of snow, Cruz called on Republicans to unite behind his candidacy and framed the contest as a one-on-one fight between him and Trump.

Still, Cruz and his allies were also keeping a close eye on Kasich, who was campaigning hard in Wisconsin and sought to project a positive message. The Cruz team was worried that Kasich might do well enough here to deprive Cruz of some delegates and gain a head of steam as the contest turns to the Northeast, seen as more favorable territory for Kasich.

But the real battle here was between Trump and Cruz, who benefited from the outright disdain that influential conservative talk radio hosts like Charlie Sykes and Jerry Bader showed toward Trump.

Bader spoke with disgust about the New York businessman at a Cruz rally in Green Bay on Sunday. The next day, Sykes appeared with Cruz in Waukesha, where the talk-show host lambasted Trump. “We have to be the firewall of common sense,” Sykes told the crowd.

Rucker reported from Washington. Jose A. DelReal in Milwaukee, Scott Clement in Washington and Robert Costa in New York contributed to this report.