By Lawrence Hurley

WASHINGTON (Reuters) - The U.S. Supreme Court on Tuesday ruled unanimously against a Puerto Rican politician who had sought to avoid a second trial on corruption charges involving a trip to Las Vegas to watch a boxing bout after his original conviction was tossed out.

It was the first ruling by the eight justices in their term that started in October. The decision was a setback to Hector Martinez Maldonado, who served in Puerto Rico's Senate from 2005 until his 2011 conviction, as well as businessman Juan Bravo Fernandez, the former president of a private security company.

Bravo Fernandez sought to bribe Martinez Maldonado to win passage of legislation that would benefit his business, according to prosecutors.

The case focused in part on allegations that Bravo Fernandez paid for Martinez Maldonado to travel to Las Vegas in 2005 to watch boxer Felix "Tito" Trinidad, a sports hero in the Caribbean U.S. territory, lose to underdog Winky Wright.

Bravo Fernandez and Martinez Maldonado were convicted for their roles in the alleged bribery scheme. But the Boston-based 1st U.S. Circuit Court of Appeals in 2013 threw out their convictions.

The Supreme Court, in an opinion written by Justice Ruth Bader Ginsburg, rejected the defendants' contention that a second trial would violate the U.S. Constitution's protection against "double jeopardy," which prevents people from being tried on charges for which they already have been acquitted.

Their lawyers argued the double jeopardy prohibition should have applied because the jury had acquitted the pair on some of the criminal charges concerning conduct closely related to the actions on which the retrial would be focused. Prosecutors maintained that the acquittals were inconsistent with the convictions, suggesting jurors did not understand the law.

(Reporting by Lawrence Hurley; Editing by Will Dunham)