Donald J. Trump won the Iowa caucuses in a landslide on Monday, a crucial first step in his bid to reclaim the Republican nomination for the third consecutive election as voters looked past his mounting legal jeopardy and embraced his vision of vengeful disruption.

Mr. Trump’s record-breaking triumph, called by The Associated Press on Monday night only 31 minutes after the caucuses had begun, gave the former president an important win in a state that had rejected him eight years ago. But on a bitter cold night, Gov. Ron DeSantis of Florida finished in a distant second place, according to The A.P., in a state where he had increasingly banked his candidacy, which nonetheless could provide him some much-needed money and momentum.

With Mr. Trump far ahead in most polls, much of the focus heading into the caucuses had been on the race for second, as Mr. DeSantis and Nikki Haley, the former ambassador of the United Nations, battled for the mantle of Mr. Trump’s chief rival. With Mr. DeSantis finishing ahead of Ms. Haley in Iowa, and her leading him in New Hampshire, the possibility of a two-person race remains elusive for Trump foes, who fear a split field will ease his path to the nomination.

Even before the Iowa results were in, Mr. DeSantis had symbolically decided to fly directly to South Carolina after Iowa instead of to New Hampshire, which votes on Jan. 23 and where Ms. Haley is making her next stand.