He played for the Baltimore Orioles, Cleveland Indians, San Francisco Giants, Seattle Mariners, Philadelphia Phillies, Pittsburgh Pirates, Colorado Rockies, and Detroit Tigers.

[1] Originally an outfielder, Mesa was signed as an amateur free agent by the Toronto Blue Jays on October 31, 1981.

He made his major league debut on September 10, 1987 against the Boston Red Sox, four days after being traded.

[7] On May 6, Mesa recorded his first career complete game shutout against the California Angels, allowing seven hits (all singles) while striking out two in the 7–0 win.

[7] However, his season began to spiral in June,[7] and he ultimately finished with a 6–11 record, a 5.97 ERA, and two complete games in 23 starts.

[1] On July 14, 1992, Mesa was traded from the Orioles to the Cleveland Indians for minor league outfielder Kyle Washington.

[1] Mesa became a relief pitcher for the Indians in 1994, and for the first season of his career, he posted an ERA better than the league average.

[1] In the postseason, Mesa allowed a game-winning home run in the 12th inning to Roberto Alomar in Game 4 of the 1996 American League Division Series against the Baltimore Orioles.

[15] In 1997, Mesa was 4–4 with 16 saves and a 2.40 ERA in 66 games, helping the Indians to their second World Series appearance in three seasons.

[16] Mesa began the 1998 season pitching in a setup role to new closer Mike Jackson, going 3–4 with one save and a 5.17 ERA in 44 games with Cleveland.

[1][17] On July 24, 1998, Mesa was traded to the San Francisco Giants along with Shawon Dunston and Alvin Morman in exchange for Steve Reed and Jacob Cruz.

[1] In the offseason, the Mariners signed Kazuhiro Sasaki to serve as closer, moving Mesa back to a setup role.

[21] Returning to the closer role, Mesa immediately found success in 2001, finishing 3–3 with 42 saves and a 2.34 ERA in 71 relief appearances.

After a strong performance in spring training, the Pirates announced that he had earned a roster spot on April 1.

[1] While with the Pirates, Mesa tied a franchise record by converting 23 consecutive save chances from August 24, 2004 until May 15, 2005.

In the book, Vizquel criticized Mesa's performance in Game 7 of the 1997 World Series, in which Mesa came in with the Indians leading 2–1 and three outs away from their first championship in 49 years, only to blow the save and allow Florida to tie the game: "The eyes of the world were focused on every move we made.

Mesa reacted furiously, pledging to hit Vizquel upon every subsequent opportunity: "Even my little boy told me to get him.