A seven-time All-Star, Pérez averaged more than 100 runs batted in per season from 1970 to 1976 for the powerful Cincinnati team that became known as the Big Red Machine for their dominance of the National League in the mid-1970s.

[6] He was signed to a pro contract in 1960 at age 17 by Cincinnati Reds scout Tony Pacheco while playing on the Camagüey sugar factory team.

That same day, he was replaced on the active roster by just-signed 19-year-old Pete Rose, who was inserted into the starting lineup at second base.

[10] In 1963 he was promoted to the Macon Peaches of the Class AA South Atlantic League, where in 69 games as a third baseman he hit .309 with 11 home runs and 48 RBIs before being promoted that same year to the Class AAA San Diego Padres of the Pacific Coast League.

The grand slam came with 2 outs and scored Vada Pinson, Frank Robinson, and Deron Johnson.

[16] Pérez's home run off future fellow Hall of Famer Catfish Hunter propelled the National League to a 2–1 victory.

[22] After his trade, the "Big Red Machine"—considered one of baseball's all-time greatest teams—sputtered and never again got into the Series, reaching the playoffs but one more time in 1979.

Sparky Anderson, the Reds manager during the championships of the 1970s, has stated in many interviews since that Pérez was the leader, and heart and soul of those teams.

In his first season with the Red Sox, he finished in the top 10 in the American League in home runs (25), RBIs (105) and intentional walks (11), and won the Lou Gehrig Memorial Award.

[22] For the 1983 season, Pérez reunited with "Big Red Machine" teammates Pete Rose and Joe Morgan on the Philadelphia Phillies.

[22] In 1984, at age 42, he became the oldest player to hit a walk-off pinch-hit home run (off the Pirates' Don Robinson).

On May 13, 1985, batting against Philadelphia Phillies' reliever Dave Rucker, he became the oldest player (44) to hit a grand slam, breaking a 70-year-old record held by Honus Wagner.

Before a game against the San Francisco Giants, Reds beat writer Hal McCoy approached Perez with an idea to bat catcher Joe Oliver in the game instead of backup catcher Dan Wilson, since Oliver hit Giants starting pitcher Bud Black well.

On May 27, 2000, in an on-field pre-game ceremony at Cinergy Field with family and former teammates and managers, the Reds retired his number, 24.

[2] In 2000, Pérez was elected to the Baseball Hall of Fame in Cooperstown, New York, garnering 385 votes on 499 ballots for a total of 77.15%, just over the three-quarters minimum required for induction.

He was inducted in July 2000 along with Sparky Anderson, Carlton Fisk, Bid McPhee and Turkey Stearnes.

[29] Pérez was inducted into the Hispanic Heritage Baseball Museum Hall of Fame in 2001 at a pre-game ceremony held at the San Francisco Giants' Pacific Bell Park.

He was proclaimed an official "native son" of Puerto Rico "for his dedication to the commonwealth as a family and community member, and for his impressive baseball accolades while representing the island."

On Saturday, a bronze statue of Pérez was unveiled near the entrance to Great American Ball Park.

[35] Tommy John thought Pérez was one of the toughest hitters he ever had to face due to his ability to hit to right-center field with power.

[39][42] Eduardo was an All-American third baseman at Florida State University and played in the College World Series.

In 2009, he managed Leones de Ponce to the Puerto Rican League championship, and in 2011 and 2012 he was hitting coach for the Miami Marlins.

In 2016, Eduardo joined SiriusXM's MLB Network Radio hosting The Leadoff Spot with Steve Phillips.

He took 17 suitcases of gifts, clothes, and medical supplies and reunited with his family in Central Violeta, Cuba—a 400-mile train ride from Havana.

In 2000, for a luncheon honoring Tony, the Marlins arranged to surprise him by helping his two living sisters, Argelia and Gloria, secure visas and come to Miami from their homes in Central Violeta, Camagüey, Cuba.

[49] Pérez advocated for many years in articles, speeches, and discussions to get Minoso elected to the Baseball Hall of Fame.