Gov. Ron DeSantis steadfastly focused his re-election campaign on President Biden rather than on his Democratic opponent in Florida. But Mr. DeSantis’s runaway victory on Tuesday, while crushing to Democrats, felt more like a win over a different rival: former President Donald J. Trump.

While candidates endorsed or handpicked by Mr. Trump stumbled nationally, Mr. DeSantis routed former Representative Charlie Crist by 19 percentage points, an astonishing result that Republicans in the state were still marveling over on Wednesday.

“We had probably the best night you could have ever asked for,” said State Senator Joe Gruters of Sarasota, the chairman of the Republican Party of Florida.

The party’s smashing success in Florida — among its brightest spots in a national midterm election with decidedly mixed outcomes — was a result of its relentless voter registration and turnout efforts there, Mr. DeSantis’s commanding campaign and Democrats’ utter collapse in a state in which they failed to effectively compete at all, leaving it to turn solidly red.

Neither Mr. DeSantis nor any other Republicans who won statewide races made mention of how vastly they outperformed many of Mr. Trump’s preferred candidates elsewhere in the country. But their winning margins spoke for themselves. When Mr. Trump took Florida in 2020, his 3.3 percentage points over Mr. Biden seemed ample in a state that had swung back and forth between Republicans and Democrats for two decades.

On Tuesday, every Republican running for statewide office won by at least 16 points, leaving little doubt that Florida is Republican country — and that Mr. DeSantis’s political career has become supercharged.

“Two more years!” some of his supporters chanted at his victory party in Tampa on Tuesday, alluding to a possible White House run in 2024.

He did nothing to dissuade them, appearing instead to encourage such speculation by giving remarks that sounded like the beginnings of a national stump speech.

“While our country flounders due to failed leadership in Washington,” Mr. DeSantis said, “Florida is on the right track.”

With the national spotlight squarely on him, Mr. DeSantis could for the first time experience intense scrutiny from the right — starting with Mr. Trump, who before Tuesday’s outcome threatened to reveal unflattering information about Mr. DeSantis if he were to challenge him in a Republican presidential primary. On Wednesday, Mr. Trump noted on his social media platform Truth Social that he netted about a million more votes in Florida in 2020 than Mr. DeSantis did on Tuesday, though he failed to mention that turnout is usually higher in presidential elections.

“There’s going to be a lot of pressure from the outside now on DeSantis politically, because he’s being widely heralded today as being the hero of the Republican Party,” said Brett Doster, a Republican strategist who advised former Gov. Jeb Bush, former President George W. Bush and Senator Mitt Romney of Utah. “What Ron DeSantis is thinking right now is, ‘OK, I’ve got to get back to governing immediately.’”

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“Anybody who’s a serious student of politics knows that the best success map for good politics is good governing,” Mr. Doster added.

In his victory speech at the Tampa Convention Center, which was packed with stylishly dressed Republicans who looked more like the political establishment than the MAGA warriors at rallies, Mr. DeSantis promised to pursue more of the muscular culture war policies that have proven popular among Republican and some independent voters.

Republicans, who won supermajorities in both chambers of the Florida Legislature, could try to eliminate most restrictions for carrying concealed weapons. They could amend a 15-week abortion ban enacted this year to prohibit the procedure earlier in pregnancy. They could expand the reach of the Parental Rights in Education Act, which bans instruction about gender identity and sexual orientation in kindergarten through third grade, to older students.

Mr. DeSantis has expressed interest in challenging First Amendment protections for the news media by rewriting libel laws. And he vowed on Tuesday to continue to oppose “woke ideology” in schools, universities and businesses.

Christopher Rufo, a conservative activist who advised Mr. DeSantis on a law known as the Stop WOKE Act, which limits how racism and other issues can be taught in schools and workplaces, said on Wednesday that the governor “has now proven that culture war is good policy and also good politics.”

“He has been the most aggressive governor on critical race theory, radical gender ideology and a host of other hot-button issues,” Mr. Rufo said. “And the voters rewarded him. I think this really lays to rest this idea that Republicans should be shying away from these issues. In fact, the evidence shows that they should be leaning in.”

After barely winning the governor’s race in 2018 against Andrew Gillum, a former Tallahassee mayor, Mr. DeSantis did not immediately begin to govern like a national conservative darling. He embarked on that trajectory only after questioning public health guidance during the coronavirus pandemic and gambling on a more hands-off approach that allowed many Floridians to maintain some sense of normalcy. More than 82,000 Florida residents have died from the coronavirus since the beginning of the pandemic.

“Ron DeSantis started to really become the figure he is today because of Covid,” said Jared E. Moskowitz, a Democrat who served as Mr. DeSantis’s emergency management chief until last year and won an open congressional seat on Tuesday. “Democrats have sold a narrative that he did a terrible job. Well, you don’t win by 19 points because you did a terrible job.”

“People are buying what he is selling,” Mr. Moskowitz added. “That may be politically inconvenient for Democrats, but it doesn’t change that it’s happening and that it’s true.”

It did not help Democrats that Republicans, who had fewer voters on the rolls until last year, spent Mr. DeSantis’s first term registering so many new members that their numbers now exceed registered Democrats by more than 300,000.

Democrats, in the meantime, failed to adequately invest in the offices, staffing and other resources necessary to reach voters in a large and expensive state. They continued to outsource basic party functions such as voter registration to outside groups whose effectiveness some Democrats have increasingly called into question.

“The day the Obama campaign rolled out of the state,” said Steve Schale, a Democratic strategist who helped former President Barack Obama win Florida twice, “rolled with it all of the infrastructure that existed.”

After Tuesday’s results, there will not be a single Democrat in statewide office for the first time since Reconstruction. On Wednesday, the Democratic Progressive Caucus of Florida called on Manny Diaz, the chairman of the Florida Democratic Party, to resign.

Mr. Diaz, who did not return a call seeking comment on Wednesday, had told some party members ahead of Election Day results that he did not intend to leave his post. On Tuesday, he released a memo showing how national Democrats abandoned the state, investing less than $1.4 million this cycle, compared with more than $58 million in 2018.

Fewer Democrats voted, and overall voter turnout dropped to about 53 percent this year, from 63 percent in 2018. In no small part because of support from Hispanic voters, Mr. DeSantis flipped solidly Democratic and Democratic-leaning counties, including Miami-Dade, Palm Beach and Osceola, home to a sizable Puerto Rican population. Mr. Crist, his opponent, won only five of the state’s 67 counties, even losing Pinellas County, where he lives.

On Tuesday, Mr. DeSantis alluded to the fact that after winning by just over 32,000 votes four years ago, he had won re-election by about 1.5 million votes.

“We set out a vision,” he said. “We executed on that vision, and we produced historic results.”