His official debut was with the Uruguayan team Wanderers de Durazno. Alzamendi played for Uruguay at the 1986 and 1990 FIFA World Cups, scoring against West Germany in 1986. He played several years for River Plate of Argentina, winning both the Copa Libertadores de América and Intercontinental Cup in 1986. On Intercontinental Cup final, Alzamendi was named as man of the match and got the only goal of the game in the 28th minute when he headed into the net after his initial shot had hit the post and then came back off the goalkeeper. That year he was also named South American Footballer of the Year.