WASHINGTON—Only white firefighters scored well enough on the test to be promoted. No blacks. So New Haven, Conn., threw out the test.

In an important reverse discrimination ruling Monday, the Supreme Court rejected that decision, cautioning employers nationwide against changing the rules once the game has begun.

New Haven discriminated against its white firefighters by ignoring the results of a promotion exam on which they did well but no African-Americans scored high enough to be promoted to lieutenant or captain, the justices said in a 5-4 ruling.

High court nominee Sonia Sotomayor had endorsed the city’s position as an appeals court judge — ammunition for both supporters and foes in her upcoming confirmation hearing.

In its last session until September, the court’s conservative majority prevailed in the ruling that faulted New Haven and the courts that had upheld the city’s decision to discard the test results. The city said it acted to avoid being sued by the minority firefighters.

Justice Anthony Kennedy said in his majority opinion that New Haven’s action amounted to discrimination based on race against the white firefighters who were likely to be promoted.

“No individual should face workplace discrimination based on race,” Kennedy said.

The ruling restricts, but does not eliminate employers’ ability to take diversity into account in employment decisions. But the ruling could make it harder for minorities to prove discrimination based solely on lopsided racial hiring or promotions.

Sotomayor and two appeals court colleagues had ruled the city did the right thing in throwing out the test, and the Supreme Court reversal gave critics fresh ammunition two weeks before her Senate confirmation hearing. Conservatives said it showed her to be a judicial activist who lets her own feelings color her decisions. “This case will only raise more questions in the minds of the American people concerning Judge Sotomayor’s commitment to treat each individual fairly and not as a member of a group,” said Sen. Jeff Sessions, R-Ala.

On the other hand, the Obama administration and liberal allies said her stance in the case demonstrated her restraint and unwillingness to go beyond precedents established by her own 2nd U.S. Circuit Court of Appeals in New York.

The high court ruling shows “she doesn’t legislate from the bench,” said presidential spokesman Robert Gibbs. “The Supreme Court clearly had a new interpretation of Title VII of the Civil Rights Act.”

Coincidentally, the justices may have given a boost to calls for quick action on her nomination.

The court said it would return Sept. 9 to hear a second round of arguments in a campaign finance case, and with Justice David Souter retiring there would be only eight justices unless Sotomayor has been confirmed by then.

In Monday’s ruling, Kennedy said, “Fear of litigation alone cannot justify an employer’s reliance on race to the detriment of individuals who passed the examinations and qualified for promotions.” He was joined in the majority by Chief Justice John Roberts and Justices Samuel Alito, Antonin Scalia and Clarence Thomas.

In dissent, Justice Ruth Bader Ginsburg said the white firefighters “understandably attract the court’s empathy. But they had no vested right to promotion and no person has received a promotion in preference to them.”

Justices Souter, Stephen Breyer and John Paul Stevens signed onto Ginsburg’s dissent, which she read aloud in court Monday. Speaking dismissively of the majority opinion, she predicted the court’s ruling “will not have staying power.”

Labor and employment lawyers suggested that companies that act to encourage and preserve racial, gender and age diversity would need to be very careful to avoid reverse discrimination lawsuits.

For example, said employment lawyer Mark Dichter, an employer might be sued under Monday’s ruling for scrapping an unannounced round of layoffs because women, racial minorities or older workers would be disproportionately affected and substituting a different analysis that affected other workers.

“If those facts came out, it would certainly support a reverse discrimination claim,” said Dichter, chairman of the Morgan, Lewis law firm’s labor and employment division in Philadelphia.