SACRAMENTO — Gov. Gavin Newsom of California, who was elected in a 2018 landslide and last year crushed a Republican-led recall, advanced easily to the general election on Tuesday, where he will face Brian Dahle, a Republican state senator.

The Associated Press called the two runoff spots about 45 minutes after polls closed in California. Mr. Dahle had a commanding lead over the other challengers in early returns, though he was trailing Mr. Newsom by a substantial margin.

The governor’s strong performance was a hint at the contest to come. Even if one candidate earns a clear majority in a race for most statewide offices, the Legislature or Congress, California’s “top two” system requires a general election runoff.

Michael Shellenberger, a Berkeley activist running as an independent, had hopes of getting past Dahle and reaching the November election. He’s known in the Bay Area as the author of “San Fransicko: Why Progressives Ruin Cities,” a critique of liberal policies on homelessness and mental illness. But Mr. Shellenberger had a fraction of the votes that Dahle had in initial returns, a confirmation that party labels still matter in the state’s open primary.

Mr. Dahle, a wheat farmer from rural Lassen County, has held state and local offices in the state’s northernmost region for more than two decades. As senator, he is personally popular within his party, and he represents close to a million Californians.

But nearly 40 million people live in California, and Democrats hold a 2-to-1 advantage over Republicans in the electorate. Although a recent poll by the Public Policy Institute of California found that half of Californians who responded felt the state was headed in the “wrong direction,” half also approved of Mr. Newsom’s performance. Solid majorities agreed with the governor’s stance in favor of abortion rights, and other polls show widespread approval of his handling of the pandemic and the economy.

Buoyed by the earnings of the state’s wealthiest taxpayers, which have boomed despite the coronavirus, California’s state budget has had a record surplus. Mr. Newsom’s fortunes also rose in the aftermath of last year’s pandemic-fueled recall, which effectively gave him an extra year to campaign and to frame himself as the champion of “California values” that were threatened during the Trump administration.

The recall eliminated the few challengers who might have posed a credible threat to the governor in the general election, giving Mr. Newsom an aura of invincibility, elevating his national profile and filling his campaign coffers. He spent election night preparing to greet President Biden and other world leaders this week at a contentious Summit of the Americas in Los Angeles.

As Californians entered the final week of voting, Mr. Dahle’s campaign had raised only about $1.4 million — substantially more than the other challengers on the primary ballot, but only a fraction of the more than $23 million raised by the governor.