Democrat Bernie Sanders also scored a sweeping victory in Wisconsin’s primary that gives him fresh incentive to keep challenging Hillary Clinton.
Sanders still lags significantly behind Clinton in the all-important delegate count.
Both parties were turning their sights toward New York, which offers a massive delegate prize in its April 19 contests. It marks a homecoming of sorts for several candidates, with Trump, Clinton and Sanders all touting roots in the state.
Trump, who has dominated the Republican race for months, suddenly finds himself on the defensive as the race moves east.
He has struggled through a series of mis-steps, including his campaign manager’s legal issues after an altercation with a female reporter and his own awkward explanation of his position on abortion.
Exit polls in Wisconsin highlighted the deep worries about Trump surging through some corners of the Republican Party. A majority of Republican voters said they’re either concerned about or scared of a potential Trump presidency, according to surveys conducted by Edison Research for television networks.
Cruz has stepped forward as the candidate best positioned to block Trump, though it would likely take a convention battle to accomplish that goal.
An ultraconservative Texas senator with a complicated relationship with Republican leaders, Cruz cast his Wisconsin victory as a “turning point” in the race and urged the party to rally around his candidacy.
“We’ve got the full spectrum of the Republican Party coming together and uniting behind this campaign,” he said.
Trump was unbowed in his defeat. His campaign put out a biting statement accusing Cruz of being “worse than a puppet – he is a Trojan horse, being used by the party bosses attempting to steal the nomination from Mr Trump.”
Sanders still trails Clinton in the pledged delegate count and has so far been unable to persuade superdelegates – the party officials who can back any candidate – to drop their allegiance to the former Secretary of State and back his campaign.
At a raucous rally in Wyoming, Sanders cast his victory as a sign of mounting momentum for his campaign.
“With our victory tonight in Wisconsin, we have now won seven out of eight of the last caucuses and primaries,” he declared. Sanders is favoured to win Wyoming’s Democratic caucuses on Saturday, but it offers a small delegate prize.
With an overwhelming white electorate and liberal pockets of voters, Wisconsin was favourable territory for Sanders. In a sign of Clinton’s low expectations in the midwestern state, she spent Tuesday night at a fundraiser with top donors in New York City.
Clinton congratulated Sanders on Twitter and thanked her supporters in Wisconsin. “To all the voters and volunteers who poured your hearts into this campaign: Forward!” she wrote.
Because Democrats award delegates proportionally, Sanders’ victory in Wisconsin did not cut significantly into Clinton’s lead in the pledged delegate count.
With 86 delegates at stake in Wisconsin, Sanders will pick up at least 45 and Clinton will gain at least 31.