As sunshine returned to Southern California on Monday, residents and officials said the region had avoided catastrophic damage from Tropical Storm Hilary, which broke records for August rainfall as it passed into California on Sunday but was much diminished from the fearsome Category 4 hurricane that had alarmed meteorologists days earlier when it was over the Pacific Ocean.

Under sheets of rain, some neighborhoods in the desert cities east of Los Angeles became a soupy mess and at one point on Monday the mayor of Palm Springs said the city was cut off by road closures. In San Bernardino and Riverside Counties, videos showed creek beds filled with sludge-colored torrents that ominously carried boulders and tree trunks.

Yet in one of the most heavily populated parts of the country — Los Angeles and San Diego Counties alone have a combined population of more than 13 million — there were no reports of deaths related to the storm as of Monday afternoon.

“I can’t remember a major storm in which we had no fatalities,” Zev Yaroslavsky, a former Los Angeles county supervisor and city councilman, said Monday. “We were prepared and, as a result, we made our own luck.”

Hilary was one of very few tropical storms to hit California over the past century. In anticipation of widespread challenges, the Los Angeles Unified School District, the nation’s second largest, had canceled classes and after-school programs on Monday. Classes were to resume Tuesday, the district said.

Crews in Los Angeles, as in other cities in Southern California and Nevada, were responding on Monday to reports of fallen trees, potholes and downed power lines, along with some road flooding. But officials generally expressed relief that things were not much worse.

“By and large, we’re feeling pretty good about it because we’re not seeing a lot of impacts to homes and residents,” said Brian Ferguson, a spokesman for the California Governor’s Office of Emergency Services. “We’re not seeing a single fatality or injury as of yet.”

Officials cautioned that some parts of the state had not yet been dug out of the mud generated by the storm. The City of Palm Desert in the Coachella Valley urged residents to use “common sense and caution” as work crews continued to respond to reports of damage. City officials said that many trees were downed and boughs broken. They advised residents to avoid parks and flooded areas.

Nearby, Michael Contreras, the chief of the Cathedral City Fire Department, said his staff rescued 46 people in 18 hours. That included 14 older residents at a board and care home who were ferried to safety with bulldozers.

In the San Bernardino Mountains, where some areas recorded more than 10 inches of rain, the storm turned roads into raging rivers filled with debris and mud. It happened so quickly on Sunday that the authorities told residents in the Forest Falls community to stay in their homes, where they were still waiting for the streets to be cleared on Monday.

State and local officials were monitoring fragile hillsides, which can still melt into a torrent of mud up to 72 hours after the clouds have cleared. “We’re not out of the woods,” Mr. Ferguson said.

In San Diego, emergency workers reported a close call: 13 homeless people were rescued from the rain-swollen San Diego River on Sunday night.

And in the mountainous Mt. Charleston area of Nevada, west of Las Vegas, residents were being advised to boil tap water before drinking it after flooding caused a severe leak in the water system.

Before reaching California, the storm dumped enormous amounts of rain on Mexico’s Baja California peninsula. Some areas recorded nearly 13 inches of rain in 24 hours, according to the country’s national coordinator of civil protection, Laura Velázquez Alzúa. The previous record was seven inches, from 1997.

Nearly 3,000 Mexican Marines were mobilized to provide aid and one person was killed by rushing floodwaters. Another was missing. But Mexico’s president, Andrés Manuel López Obrador, posted in Spanish that “fortunately, there was not much damage.”

At a time of year when Southern California is normally dangerously desiccated and very vulnerable to wildfires, some meteorologists and engineers pointed to the positive effects of the drenching rains.

Officials in Los Angeles County touted the success of projects that had sought to divert and store rainwater. As of Monday morning, Los Angeles County had captured enough storm water to supply at least 33,600 residents for a year, said Steve Frasher, a public works spokesman.

And the storm was helping to dampen fire risks in Southern California, said Daniel Swain, a wildfire expert at the University of California, Los Angeles. “There’s likely to be a prolonged reprieve in Southern California,” he said in an online briefing. “Enjoy it while you can.”

For homeowners who suffered flood damage, cleanup will be complicated by an extra challenge: In a part of the country not accustomed to tropical downpours, less than 1 percent of households have federal flood insurance. Home insurance policies typically don’t cover flooding.

In Palm Springs, no more than 167, or 0.7 percent, of the city’s roughly 24,000 households have flood insurance policies, according to data from the Federal Emergency Management Agency, which runs the federal program.

But in parts of California closer to the coast, some were puzzled at why the storm had received so much attention.

As the air cleared on Tuesday, Vazken Kouftaian, 40, a resident of Santa Clarita, north of Los Angeles, took his 2-year-old son for a walk. This storm, he said, felt more like a normal rain shower. “They were expecting something very bad,” he said. “But it was nothing like that.”

Reporting was contributed by Corina Knoll from Los Angeles; Vik Jolly from San Diego; Rick Rojas from Las Vegas; Maggie Miles from Palm Springs, Calif.; Emiliano Rodríguez Mega from Mexico City; Sergio Olmos from Cathedral City, Calif.; Soumya Karlamangla from San Francisco; Shawn Hubler from Sacramento; Christopher Flavelle from Washington; and Anna Betts from New York.