Donald J. Trump’s victory in the New Hampshire primary on Tuesday provided him the second of an opening pair of wins in the Republican nomination fight that accelerated his push for the party to coalesce behind him and deepened questions about the path forward for Nikki Haley, his lone remaining rival.

The defeat of Ms. Haley in New Hampshire came eight days after the former president trounced Gov. Ron DeSantis of Florida so thoroughly in Iowa that it drove Mr. DeSantis from the race. Mr. Trump and his allies have turned his twin early wins into a milestone — declaring, after just the first two contests, that the party needs to unite behind him now to prepare for a rematch in November between Mr. Trump and President Biden.

No Republican candidate has ever won the first two states and then not ultimately secured the presidential nomination, a fact that Mr. Trump himself noted in his victory speech in Nashua, N.H.

“When you win Iowa and you win New Hampshire, they’ve never had a loss — there’s never been — so we’re not going to be the first, I can tell you,” Mr. Trump told the crowd.

Regardless of what comes next, the win on Tuesday sealed Mr. Trump’s status as the party’s standard-bearer in the history books: Before Mr. Trump, the only Republicans who have ever won both the Iowa caucuses and the New Hampshire primary have been sitting presidents.

The race was called on Tuesday night by The Associated Press the moment the last polls closed, sapping any drama from the outcome. Minutes later, Ms. Haley raced to speak first at her own election party in Concord, N.H., forcefully pressing her case that nominating Mr. Trump would be tantamount to conceding the general election to Democrats.