Saprissa took the trophy -- the North Central American and Caribbean equivalent of Europe's Champions League - for the third time 3-2 on aggregate after last week's 2-0 home victory.
The club also winners in 1993 and 1995 are coached by former Costa Rica forward Hernan Medford and owned by flamboyant Mexican businessman Jorge Vergara who also owns Mexico's most popular club Guadalajara.
Wednesday night's defeat capped a unhappy opening half of the year for UNAM who are coached by former Real Madrid and Mexico striker Hugo Sanchez and had made a trip to Japan their priority.
The Pumas who had won the last two Mexican championships finished bottom of their group in the Clausura championship and ending Sanchez's much-publicised dream of winning five consecutive titles.
Sanchez joined the protests as furious UNAM players surrounded U.S. referee Kevin Stott at the end of the match. The official was given a police escort off the field.
The Pumas had several penalty appeals turned down during the game.
Saprissa went ahead after 32 minutes when Ronald Gomez scored with a left-foot shot inside the area from a pass by Alonso Solis.
Veteran striker Joaquin del Olmo pounced on a defensive mix-up to equalise in the 65th minute but by the time Brazilian Leandro scored again three minutes into injury time it was too late.
The visitors played the last 18 minutes with ten men after Alan Aleman was sent off for a foul on del Olmo.