If there was any question whether Donald J. Trump was on track to win the Republican nomination, it was answered Monday night by the voters of Iowa.

The first-in-the-nation Iowa caucuses delivered him a sweeping victory, offering the most concrete proof yet of his dominance over the Republican Party.

With nearly all the votes counted, Mr. Trump’s share was 51 percent. Ron DeSantis finished a distant second at 21 percent, with Nikki Haley at 19 percent.

The result is not surprising or even unexpected, but Mr. Trump’s victory is no small feat. A year ago, Iowa did not look as if it would be easy for the former president. In an upset eight years ago, Iowa voters rejected Mr. Trump in favor of Ted Cruz. And unlike the rest of the country, the Iowa political establishment has refused to get in line behind Mr. Trump.

Not only did he win in a landslide anyway, but his 30-point margin of victory set a record for a contested Iowa Republican caucus.

Better still for Mr. Trump, neither Mr. DeSantis nor Ms. Haley posted a strong second-place showing that might have bestowed clear momentum for future races. If anything, Mr. DeSantis’s second-place finish might dampen Ms. Haley’s momentum heading into New Hampshire.

Mr. Trump’s decisive victory was built on his usual — if still remarkable — strengths among working-class and rural voters, who made up a preponderance of the Iowa electorate. In county after county across the Iowa countryside, Mr. Trump obtained more than 60 percent of the vote — and sometimes 70 percent — with his rivals languishing in the teens or single digits. He also excelled among white evangelical Christians and self-described “very conservative” voters — two groups that held him back here eight years ago. It’s a coalition that naturally gives him a commanding advantage in a party that’s disproportionately conservative, working class, evangelical and rural. It was enough for him to win all but one of the state’s counties, with his one defeat by a single vote in Johnson County.

Mr. DeSantis was dealt a serious setback to his already ailing candidacy. He seemed like a perfect fit for Iowa, as the caucus electorate usually favors ideologically conservative candidates. He followed the winning caucus playbook, including campaigning in all 99 counties and earning high-profile endorsements from the state’s governor, many other elected Republicans in the state and prominent evangelical leaders. None of it seemed to make a difference.

The road ahead for him is bleak. No upcoming contest plainly offers Mr. DeSantis a better chance of victory, and his poll numbers are even weaker in the states ahead. If he can’t compete in Iowa, it’s hard to imagine where he can. It has raised the question of whether he will continue in the race, though he has said he’s staying in. Either way, Ms. Haley has overtaken Mr. DeSantis as Mr. Trump’s nearest, if still distant, rival.

For Ms. Haley, the third-place finish is a disappointment but not dire. She showed important strength among college-educated, independent and suburban voters, who have long been Mr. Trump’s greatest skeptics. She defeated Mr. Trump by a comfortable margin in precincts where a majority of residents hold a four-year college degree. She also won 64 percent of self-described moderates.

Ms. Haley’s strength among moderates and college graduates wasn’t enough for second in Iowa, as several late polls suggested, but voters like these will represent a much larger share of later primary electorates. It might just be enough for her to compete in relatively well-educated states with larger numbers of independent voters, including New Hampshire next week — where the polls already show a close and tightening race.

But the results also confirmed that her appeal is extraordinarily narrow, all but confined to those moderate and highly educated voters. She routinely failed to reach 10 percent of the vote in rural, working-class precincts. The entrance polls found that she won just 9 percent among voters who never attended college.

College-educated and independent voters can only take a candidate so far in a working- class Republican Party. It certainly didn’t take her very far in Iowa on Monday night. There is no path for Ms. Haley to win the nomination without greatly expanding her appeal among these base constituencies.