LOS ANGELES — Representative Karen Bass and billionaire developer Rick Caruso breezed past a large field of rivals looking to be the next mayor of Los Angeles and advanced Tuesday to a runoff election in November.

An early tally of mail-in ballots showed Mr. Caruso with 41 percent and Ms. Bass with 38 percent. A candidate needed to top 50 percent to avoid a runoff.

A dozen names were on the ballot, though several candidates dropped out.

Ms. Bass, a favorite of the party’s progressive wing, and the Republican-turned-Democrat Caruso easily distanced themselves from the rest of the field. City Councilman Kevin de Leon, a former state Senate leader, was a distant third with 7 percent.

Ms. Bass, who was on President Biden’s shortlist for vice president, would be the first woman mayor of Los Angeles and the second Black person to hold the office.

The race largely focused on homelessness and crime. More than 40,000 people live in trash-strewn homeless encampments and rusty RVs, and widely publicized smash-and-grab robberies and home invasions have unsettled residents.

Each candidate used their victory speeches to promise a better tomorrow while also taking shots at their opponent.

“Together we will make a city where you want to live because you feel safe, because the air you breathe is clean, and because people are no longer dying on our streets,” Ms. Bass said. “Not with empty promises from the past, but through a bold path forward.”

Mr. Caruso quoted Bass as saying that under her leadership homelessness would not be solved in her first term and that the most residents could count on would be “light at the end of the tunnel” after four years.

“Whoa. Whoa,” Mr. Caruso said. “Let me respond by saying this: The light at the end of the tunnel is shining bright tonight.”

Mr. Caruso, 63, who sits on the board of the Ronald Reagan Presidential Foundation and was endorsed by the police union, has positioned himself as a centrist outsider running against City Hall’s progressive establishment. He blames Ms. Bass, 68, and other longtime incumbents for sprawling homeless encampments that have spread into virtually every neighborhood and concerns about unsafe streets.

“This is a great night because so many people have gone to the voting booth, and they’ve sent a message: We are not helpless in the face of our problems,” Mr. Caruso said. “We will not allow this city to decline. We will no longer accept excuses.”

His strong performance is an unwelcome sign for Democrats defending their fragile majorities in Congress and in other races around the country.

The last time City Hall veered to the political right was in 1993, when voters turned to Republican businessman Richard Riordan to lead the city in the aftermath of the deadly 1992 riots that erupted after four white police officers were acquitted of assault in the beating of Black motorist Rodney King.

Los Angeles, however, is much changed since Mr. Riordan’s days. It’s more Latino, less white and more solidly Democratic. Only 13 percent of registered voters are Republicans.

Mr. Caruso’s estimated $4.3 billion fortune allowed him to run a seemingly nonstop display of TV and online ads. His campaign’s spending — over $40 million as of early this week, most of it his money — topped all other candidates combined.

“It’s hard to defeat a people-powered campaign … no matter how much money is spent, and it’s hard to defeat folks who are committed to a cause, not just a candidate,” Ms. Bass said. “All of us stood strong against an onslaught, a $45 million onslaught to be exact, spent by a billionaire.”

By comparison, Ms. Bass’ spending hit about $3.3 million, though both campaigns were also supported by ads from outside groups.

There was competition over celebrity endorsements, as is typical in Los Angeles. Earvin “Magic” Johnson backed Ms. Bass, while Mr. Caruso had Snoop Dogg and Gwyneth Paltrow behind him.

The race took a nasty turn recently.

Ads run by Ms. Bass and her allies depict Mr. Caruso as a West coast version of President Trump, who is dodging taxes, blowing a “right wing dog whistle” and lying about Ms. Bass’ record.

In advertising from Mr. Caruso and his supporters, Ms. Bass emerges as an ethically compromised charlatan who missed key votes in Congress and counts an indicted city councilman in her circle of friends.