Consumers who say they were wrongfully charged overdraft fees won class-action status Tuesday in their lawsuit against a San Francisco bank, the first in a series of cases pending against some of the nation’s largest financial institutions.

The suit claims that Union Bank processed debit-card transactions from largest to smallest, rather than chronologically, to increase the risk that customers would overdraw their checking accounts.

Cynthia Larsen of Riverside, Calif., said the bank charged her three overdraft fees of $32 each in 2009. If her purchases had cleared in the order she made them, she would have overdrafted once, she said.

According to her attorney, the bank estimated that reordering transactions would generate $18 million in fees annually.

A spokesman for Union Bank declined to comment, citing the pending litigation.

The case is part of multidistrict litigation, involving about 30 banks, that is before U.S. District Judge James Lawrence King in the Southern District of Florida.

Bank of America agreed to settle its suit for $410 million this year.

The judge has yet to decide the status of the cases against Chase and U.S. Bank, among others. But co-lead attorney Bruce Rogow of the Alters Law Firm said that Tuesday’s action sets the stage for similar decisions.

Rogow said the class could encompass hundreds of thousands of consumers charged millions of dollars in fees. Last year, Wells Fargo was f orced to return $203 million to consumers after it lost a separate class-action suit.

“All the banks will fall, ultimately,” Rogow said. “The class certification order is a precedent that will apply to all of the other banks because they all engaged in the same practice.”

Overdraft fees have long been a target of consumer advocates, who say they unfairly punish low-income people.

Last year, after a public outcry over the charges and congressional scrutiny, the Federal Reserve instituted rules that largely prohibited banks from allowing customers to overdraw their accounts and get hit with a fee unless they signed up for the service.

Although the Fed rules did not address the order in which transactions are processed, many banks have dropped the practice — or discontinued their overdraft programs altogether.

Still, the service remains popular with some people. The financial consulting firm Moebs Services said that about 77 percent of bank customers have opted in.

Based on first quarter results, overdraft revenues would be $30 billion, the lowest level since 2006.