DES MOINES — Senator Ted Cruz of Texas, powered by a surge of support from evangelical Christians, dealt a humbling loss to Donald J. Trump in the Iowa caucuses on Monday, throwing into question the depth of support for Mr. Trump’s unconventional candidacy.

In the first contest of what so far has been more a populist revolt against the political order than a traditional Republican primary, Senator Marco Rubio of Florida finished a strong third, bolstering his case to consolidate the support of Republicans uneasy about the two top finishers.

With 98 percent of precincts reporting, Mr. Cruz had nearly 28 percent of the vote, Mr. Trump 24 percent and Mr. Rubio 23 percent.