Mark Wong recently had a client fall hard for a 5,000 square foot home in Los Altos Hills — big yard, great schools, plenty of room for family and a remote office.

The property went up for sale at just under $5 million. Hoping to overwhelm other buyers, Wong’s client bid $6 million. But the home, on a one-acre lot, drew 16 offers and sold for $6.75 million.

“We went $1 million over the asking price and we weren’t even close,” said Wong, a Compass real estate agent in Saratoga. “Once again, Silicon Valley real estate is defying gravity.”

Across the Bay Area, home prices continued to surge in October, with all nine counties reporting double-digit growth and pushing the median price of an existing single family home to $1.12 million, according to CoreLogic data. Alameda County — up 20% to $1.15 million from the same month last year — led the boom, followed by Napa (up 19% to $825,000) and Solano (up 18% to $555,000) counties.

Prices in Santa Clara County climbed 16.5% to $1.55 million, jumped nearly 11% in San Mateo County to $1.74 million, and rose 11.6% to $1.75 million in San Francisco, according to the real estate data and services company.

CoreLogic economist Selma Hepp said the increasing Bay Area prices could be due to the growing number of expensive homes selling.

Demand has been strong in the Bay Area and across the country, she said, driven by an influx of millennials into the market and the easing of international travel restrictions, allowing new workers to once again settle in the U.S. In other parts of the country, investors have been aggressively buying up single family homes.

“In theory, we will run out of buyers at some point,” Hepp said. “But maybe it doesn’t apply in this case.”

U.S and Bay Area housing supply could be further pinched by shortages of material and labor to build new homes, she said.

As prices climb, more prospective buyers have been shut out. The run-up in Bay Area prices has made it the least affordable region in California.

The median household income needed to purchase a Bay Area home rose to $235,000 in September, nearly triple the wages needed in early 2012, according to the California Association of Realtors. A decade ago, about 45% of families could fit a Bay Area home purchase into their budget; now, just 22% can afford it.

By comparison, roughly half of U.S. households have enough income to buy a home.

Agents say Silicon Valley’s high prices have been driven by well-paid tech workers, low interest rates and a scarcity of homes for sale. Agents are rolling up a record year while affordability scrapes to near record lows.

Rising prices have cooled some demand, agents say, but deep-pocketed buyers continue to pursue suburban properties. In many attractive markets, homes are selling within a week or two of being put up for sale.

“Today’s buyers are all qualified to buy $2 million homes,” said Cupertino agent Ramesh Rao.

He sees Silicon Valley buyers more interested in accessory dwelling units for in-laws or rental income. But Rao has also seen some older residents resisting the urge to sell and downsize, limiting the available homes for sale. “Nobody wants to sell,” he said. “It’s just a comfort zone.”

The Alameda County market has reached record levels.

“The demand just outstrips supply,” said Jeffrey Neidleman, an Oakland agent and president of the Bridge Association of Realtors. Buyers have not been deterred by several high-profile crimes in some Oakland neighborhoods, he said.

Overall, upscale cities and neighborhoods in Alameda County have driven the market — Piedmont, Berkeley and Oakland communities near Montclair have been popular, Neidleman said.

One family recently was looking to trade up for more room, and found a restored four-bedroom home in the Berkeley flats listed for $1.95 million. The home came with a backyard accessory dwelling unit that could be used as a rental or an in-law suite.

The sellers accepted a $2.7 million pre-emptive offer, he said. “Berkeley is just insane right now.”

Wong, too, is having a record year in the super-heated and competitive Silicon Valley market. Even properties near major highways that need renovations are getting heavy interest from tech buyers, he said. “That’s the market right now.”