DENVER — Expanding a streak of legal victories for same-sex marriage, a federal appeals court ruled on Wednesday that states may not deny same-sex couples their “fundamental right” to marry, overturning Utah’s voter-approved ban on such unions.

Advocates for same-sex marriage hailed the 2-1 decision by the United States Court of Appeals for the 10th Circuit here in Denver as a historic win. It had special resonance because it sprang from a legal challenge that brought jubilant scenes of gay nuptials to the socially conservative Utah heartland in December, when a lower court first struck down the state’s ban.

Since then, judges from Arkansas to Michigan to Idaho have tossed out prohibitions on same-sex marriages, with the most recent ruling coming Wednesday as a federal judge struck down Indiana’s ban. But legal observers said the Utah ruling was significant because it was the first time a federal appeals panel had found that same-sex couples have a constitutional right to marry.

“They desire not to redefine the institution but to participate in it,” Judge Carlos F. Lucero, nominated by President Bill Clinton, wrote in the majority opinion. Judge Jerome A. Holmes, nominated by President George W. Bush, joined Judge Lucero in striking down Utah’s ban, while Judge Paul J. Kelly Jr., a nominee of the elder President George Bush, dissented.