Open houses are drawing crowds and multiple offers across the Bay Area as buyers send prices soaring in a competition for the scant number of homes for sale.

March marked more than 20 consecutive months of year-over-year price gains for single-family homes in the East Bay, South Bay and Peninsula, according to real estate information service DataQuick, which released a report on March sales Wednesday. But the number of March sales in the Bay Area was the lowest in six years, an indication of how little is on the market.

The San Diego-based company said that prices were up 29.2 percent from the previous March in Alameda County to $575,000. In Contra Costa County, prices rose 22.8 percent to $425,000. Santa Clara County gained 20.3 percent to $800,000, and San Mateo County was up 13.2 percent to $860,000.

"There is just such a huge pent-up demand," said Margaret Garber-Teeter with Alain Pinel Realtors in Walnut Creek. An open house she held on Sunday in Walnut Creek drew more than 100.

In exclusive Piedmont in Alameda County, a four-bedroom, five-bath, 3,704-square-foot home sold for more than $1 million over asking price.

"It was on the market for less than a week," said Jane Anderson of The Grubb Co. Realtors, who handled the sale.

The home was priced at $2.95 million and sold for $4.015 million. It was on more than an acre, a rarity in the upscale, established community, she said.

One home in West San Jose recently drew 56 offers and sold for $1.33 million -- $400,000 over the asking price.

"That house was a tear-down," said Barbara Stewart, the Los Gatos broker who handled the sale. "There are so many people that want to take those tiny little houses and build mansions on them."

The home's big appeal was the coveted Cupertino Union School District, a strong draw for buyers with young children. The home had a roof that leaked and needed other major repairs. Listed for $925,000, no offer was for less than $1 million, Stewart said.

"It's an amazing market," said Mark Wong of Alain Pinel Realtors in Saratoga. Offers of $400,000 or more over asking price are common, he said.

Charles Enzwiler, 32, who works for an online tech site, gave up looking for a house to buy in Contra Costa County last year because of the frenzied competition.

"Before I could step my foot into a place, it had already been shown 40 times and that was two days after it had been on the market," he said.

Enzwiler and his wife, Jennifer, started looking again three weeks ago, finding more for sale in the $400,000 price range. That could be a sign that inventory will improve in April.

"There's extremely strong buyer demand, but up until now very little inventory," said Glen Bell of Better Homes and Gardens Real Estate in Berkeley. "We see that changing a little only in the last week."

With so few homes on the market, March single-family home sales were down from a year ago in the nine-county Bay Area to the lowest level since 2008, and the second lowest level since at least 1988, when DataQuick began keeping records. But sales were up from February, which is typical as the home buying season kicks off.

"Our inventory levels are still incredibly low," said Quincy Virgilio, chairman of MLSListings in San Jose, which tracks inventory in the South Bay. "Even though there's probably 600 to 700 more properties for sale than in January, we're still at about half of normal."

In Contra Costa County, price gains have shrunk the supply of homes for sale for less than $300,000, according to Marilyn Cunningham, president of the Contra Costa Association of Realtors. That's made it tough on first-time buyers, she said.

"If I have client that's a first-time buyer and they want to look under $300,000, that knocks out Concord," Cunningham said. "The house you could buy a year ago for $250,000 to $300,000 is now selling for $425,000. It's the same in Martinez."

According to DataQuick, sales in Contra Costa County of all types of homes -- condos, townhomes and single-family detached homes -- for under $300,000 were down 53.2 percent from a year ago.

At the same time, sales for over $500,000 were up 15.6 percent and up 33.6 percent for homes priced at more than $800,000.

The Contra Costa Association of Realtors said there's hope -- its latest figures show the inventory of homes has begun to grow.

"For the first time in recent memory, supply is poised to outstrip demand," the association reported.

In Santa Clara County, sales of all types of homes for less than $500,000 were down 31.5 percent from a year ago, while sales for more than $500,000 rose nearly 12 percent. Sales of homes for more than $800,000 were up 23.2 percent in March.

Contact Pete Carey at 408-920-5419 Follow him at Twitter.com/petecarey.