Mr. Sanders’s victory leveraged his own reliable strengths as a liberal champion against a moment of turmoil in the party’s more moderate wing: With Mr. Biden tumbling and Mr. Buttigieg and Ms. Klobuchar striving to take his place, Mr. Sanders’s grip on progressives carried him to the top of the field in both Iowa and New Hampshire.
But in both states he captured less than 30 percent of the vote, and his vote share was the lowest total ever for a winner in the primary here. Coupled with the abrupt rise of Mr. Buttigieg and Ms. Klobuchar, his modest success only underscored the churning uncertainty of the race and raised the prospect of a drawn-out nominating process that could last through the spring.
“This victory here is the beginning of the end for Donald Trump,” Mr. Sanders told jubilant supporters in Manchester, N.H., claiming “a great victory” even before the final results were in. And looking toward Nevada and South Carolina, the next two states to vote, he vowed he would “win those states, as well.”
The rise of Mr. Sanders, a democratic socialist from Vermont who remains a political independent, has distressed many centrists and traditional liberals at a time when Democratic voters are united by a ravenous desire to defeat President Trump. Mr. Trump’s impeachment acquittal, the chaotic vote-counting in Iowa and the fractured Democratic field have many in the party worried that they are endangering their opportunity to win back the White House.
Yet for Mr. Sanders, 78, winning here and cementing his status as a front-runner represented a moment of redemption just four months after he had a heart attack that threatened his candidacy, and four years after he lost the Democratic nomination after a long and often bitter primary race.
While he has not demonstrated a capacity to appeal much beyond his left-wing base, Mr. Sanders is benefiting from something he lacked in 2016: a field of opponents who are dividing moderate voters. The centrist candidates, so far, have been unable to consolidate support.
Mr. Buttigieg and Ms. Klobuchar asserted themselves on Tuesday, and their rivalry may only intensify; Mr. Biden is fading but staying in the race; and the self-funding Michael R. Bloomberg, the former mayor of New York City, is gaining strength in advance of the Super Tuesday contests next month.