He played as a catcher in Major League Baseball (MLB) for the Kansas City Athletics, Cleveland Indians, and Texas Rangers from 1966 to 1973.

After his All-American college baseball career with Florida State University, Suarez signed with the Athletics.

As well as being the catcher for the Jesuit Tigers, Suarez played for West Tampa's American Legion team with Lou Piniella and Tony La Russa.

[2] Suarez attended Florida State University, and took over catching duties for the Seminoles baseball team as a sophomore in 1963.

[6] That season, he batted .253 with thirteen home runs and twenty RBIs while providing excellent defense for the Broncs and Double-A Birmingham Barons.

He hit his first major league home run in his first start of the season against Mickey Lolich of the Detroit Tigers.

[9] Suarez did not receive much playing time in Cleveland, appearing in only seventeen games in 1968, two of which were out of his natural position in extra inning affairs.

The Indians traded Suarez with Roy Foster, Rich Hand, and Mike Paul to the Texas Rangers for Del Unser, Denny Riddleberger, Terry Ley, and Gary Jones at the Winter Meetings on December 2, 1971.

He platooned with Dick Billings behind the plate in 1973, and produced a .248 batting average while establishing himself as one of the better fielding catchers in the American League.