Aspromonte graduated from Brooklyn's Lafayette High School and made his pro debut in the Class ASally League. In September 1956, the pennant-bound Dodgers placed him on their roster, and on September 19, during a 17–2 triumph over the St. Louis Cardinals at Ebbets Field, Aspromonte made his MLB debut at age 18, striking out as a pinch hitter for Sandy Amoros in the eighth inning. It was Aspromonte's lone appearance in a Brooklyn uniform: he spent the next three seasons in minor league baseball before making the 1960 Los Angeles Dodgers roster out of spring training. On May 5, 1960, his four hits in five at bats, including his first major league home run, led the Dodgers to a come-from-behind win over their rival, the Milwaukee Braves. However, he spent most of the season in Triple-A, where he batted.329 in the American Association. The following year,, was Aspromonte's first full season in the major leagues. He appeared in 47 games, starting two at third base and three at shortstop, and he hit.241 with two runs batted in in 62 plate appearances. The Dodgers exposed him to the 1961 Major League Baseball expansion draft, and he was selected by the Houston Colt.45s with their second selection, the third player taken overall. On April 10, 1962, Aspromonte, playing third base and inserted into the leadoff position, became the first batter in Houston's MLB history. He singled to left field off Don Cardwell of the Chicago Cubs for the club's first hit, then scored its first-ever MLB run when the next batter, Al Spangler, tripled. Aspromonte would score two more runs that day, as the Colt.45s beat the Cubs, 11–2. Aspromonte was the starting third baseman for the Houston franchise for its first six seasons, and led National Leaguethird basemen in fielding percentage on two occasions. He twice batted over.280 and reached double-digits in home runs. In, he lost his starting third base job to Doug Rader. He was a backup third baseman and utilityman for the 1968 Astros and the 1969–70 Braves before his final season. He returned to New York City at age 32 when the Braves traded him to the Mets for Ron Herbel on December 1, 1970. He started 93 games at third base for the 1971 Mets, twice as many as former regular Wayne Garrett. But Aspromonte batted only.225 with five home runs. In his final game, the last Brooklyn Dodger to play in the major leagues went hitless in three at bats, with an RBI, against the Cardinals' Steve Carlton at Shea Stadium. Aspromonte collected 1,103 hits in his major league career, with 135 doubles, 26 triples and 60 home runs. As of 2018, Aspromonte holds the club record for grand slams. He resides in Houston, Texas. On January 26, 2019, it was announced that Aspromonte would be an inaugural member of the Houston Astros Hall of Fame and is set to be inducted on August 3, 2019.