Tavárez began his professional career on March 16, 1990, signing a minor league contract with the Cleveland Indians organization.

Tavárez progressed rapidly the following year, playing in Kinston, Canton-Akron, and finally with the Cleveland Indians.

He was named the Indians' 1994 Minor League Player of the Year (receiving the "Lou Boudreau Award").

Tavárez was the Sporting News American League Rookie of the Year, but finished sixth in the ballot by the Baseball Writers' Association of America.

He was suspended for three days after a brawl in Milwaukee and spent two weeks in Triple-A Buffalo before appearing in the ALDS.

Tavárez was traded to the San Francisco Giants on November 13, 1996, along with infielders Jeff Kent and José Vizcaíno and a player to be named (pitcher Joe Roa) in exchange for third baseman Matt Williams and a player to be named (outfielder Trenidad Hubbard).

He also was placed on the disabled list for the first time after straining a latissimus dorsi muscle and received his second suspension after an argument with umpire Sam Holbrook.

On October 6, against the Pittsburgh Pirates, Tavárez struck out nine hitters and took a no-hitter into the eighth inning before it was broken up by Mendy López.

Tavárez was relegated to bullpen duty in 2003 after being signed by the Pittsburgh Pirates as a minor league free agent on January 28.

He had allowed a solo home run to Carlos Beltrán, issued two walks, and hit a batter.

Tavárez suffered the loss against the Boston Red Sox in Game 1 of the 2004 World Series, giving up the game-winning home run to Mark Bellhorn in the eighth inning.

A free agent following the 2005 season, Tavárez agreed to a two-year, $6.7 million deal with the Boston Red Sox on January 18, 2006.

[11] In spring training, it had been assumed that Tavárez was simply holding the fifth spot in the rotation for the Red Sox top pitching prospect Jon Lester while he recovered from cancer.

[18] On March 13, 2009, Tavárez signed a minor league contract with the Washington Nationals and was invited to Spring Training.

[22] After playing baseball for 19 years, at the minor and major league level, Tavárez decided to retire in 2009.