Workers can’t sue under a federal job-bias law to claim they are underpaid because of gender or race discrimination that occurred years earlier, a divided U.S. Supreme Court ruled in a victory for employers.

The justices, voting 5–4, rejected a $360,000 award to Lilly Ledbetter, an Alabama Goodyear Tire & Rubber Co. worker who said almost two decades of discrimination meant her salary was 15% to 40% lower than what her male counterparts earned.

The 1964 Civil Rights Act typically gives workers 180 days from the time of the alleged discrimination to file a complaint with the Equal Employment Opportunity Commission. The question was whether workers can claim that their most recent paychecks are affected by bias that took place outside the 180-day window.

“Current effects alone cannot breathe life into prior, uncharged discrimination,” Justice Alito wrote for the majority. “Ledbetter should have filed an EEOC charge within 180 days after each allegedly discriminatory pay decision was made and communicated to her.”

Chief Justice Roberts and Justices Scalia, Kennedy, and Thomas joined Justice Alito’s opinion. Lower courts were divided on the issue.

Justice Ginsburg, the court’s only woman, took the unusual step of reading a summary of her dissent from the bench as she sat next to Justice Alito. She said the majority “does not comprehend, or is indifferent to, the insidious way in which women can be victims of pay discrimination.”

“Today’s decision counsels: Sue early on, when it is uncertain whether discrimination accounts for the pay disparity you are experiencing,” Justice Ginsburg said.

The ruling left open the possibility that women can win similar claims under a different law, the Equal Pay Act, which lets female workers sue when male counterparts receive higher wages for doing the same work. That measure, however, doesn’t cover other types of discrimination, such as racial bias.

“The opinion matters much more for folks bringing race discrimination claims or religious discrimination and the like,” said Kevin Russell, a partner at Howe & Russell in Washington who represented Ms. Ledbetter. “They have no alternative” to the Civil Rights Act.

Ms. Ledbetter originally invoked the Equal Pay Act as part of her lawsuit, later dropping that claim. Whether she would have succeeded under that law isn’t clear.

The Equal Pay Act is of limited use in cases pressed by individuals, according to Neal Mollen, an employment law attorney at Paul Hastings Janofsky & Walker in Washington. The law is typically invoked to compare the pay of a predominantly female class of workers with a largely male group doing a similar job, he said.

Mr. Mollen, who filed a Supreme Court brief backing Goodyear on behalf of the U.S. Chamber of Commerce, said yesterday’s ruling has “great importance for employers.”

The Supreme Court in 2002 said workers who object to particular hiring, firing or promotion decisions are bound by the 180-day deadline. At the same time, the court said workers alleging a different type of discrimination, known as “hostile work environment,” may get damages for years-old wrongdoing that is part of a “continuing violation.”

Mr. Ledbetter worked at Goodyear’s Gadsden, Ala., plant from 1979 to 1998, when she took early retirement. She filed her complaint with the EEOC in March 1998.

Goodyear, while acknowledging that Ms. Ledbetter was paid less than men holding similar jobs, attributed the disparity to her poor performance over the years. The company put in place a merit-based compensation program in 1982.