From 1968 through 1977, he played for the Boston Red Sox, Chicago White Sox, St. Louis Cardinals, Cleveland Indians (1974), New York Mets and Detroit Tigers. Alvarado batted and threw right handed. In a nine seasons, he posted a .214 batting average with five home runs and 84 RBI in 463 games played.
Nicknamed "Timba", Alvarado broke in the majors in 1968 with the Boston Red Sox. In 1969 he started at Triple-A with the Louisville Colonels, and led the International League in runs (89) and hits (166), garnering Most Valuable Player honors. He returned to the Red Sox at the end of the season.
A competent infielder with a strong arm, Alvarado divided his playing time between shortstop and second base. After hitting .224 in 59 games for Boston in 1970, he was traded to the Chicago White Sox along with Mike Andrews in the same transaction that brought Luis Aparicio to the Red Sox. His most productive season came in 1972, when he posted career-highs in runs (30), hits (57), doubles (14) and games (103). He also played in parts of five seasons with the Cardinals, Indians, Mets and Tigers, until his retirement in 1977. A very valuable backup infielder, he never batted above .216 in a season.
Alvarado died in his hometown of Lajas, Puerto Rico, at the age of 52.