WASHINGTON — A group of Holocaust survivors and their families notched a crucial victory on Friday, as Congress approved legislation that would make it easier to reclaim art confiscated during World War II.

The unanimous vote — which came during a late-night session as the Senate worked to pass a spending bill to avert a government shutdown and wrap up its business for the year — was the culmination of a bipartisan effort to help victims whose art was taken by the Nazis and their allies. The House passed the bill on Wednesday.

Should President Obama sign it into law, as expected, the measure would loosen, and standardize across the country, the statute of limitations on claims for the return of looted art. Survivors and their families would have six years to make a claim after identifying pieces taken from them and proving their right to them.

The legislation is considered a critical tool as Holocaust survivors and their heirs have faced a bureaucratic and legal tangle of governments, museums and collectors to recover art taken from them more than 70 years ago. In many cases, the works are now in museums or private collections, complicating the fight over ownership.