The younger brother of Andy Cohen, Syd saw limited action as a relief pitcher for the Washington Senators over the course of three major league campaigns. He made his major league debut at the tail end of the 1934 season and became the last American League pitcher to both serve up a home run to Babe Ruth and to strike him out. Syd also enjoyed particular success against Lou Gehrig, whom he struck out five times in seven at-bats. Before his major league career, Cohen played in the Mexican League at a time when the locals were demanding more Mexican players on the team. Thanks to his swarthy appearance and his flawless Spanish (he was raised in El Paso), the team introduced him as Pablo Garcia, and he played under that pseudonym. When he returned to the Mexican League as a coach many years later, the fans still called him Pablo. Cohen Stadium in El Paso, Texas, is named for Syd and his older brother Andy, who also played major league ball. It is believed to be the only professional baseball stadium named for a Jewish ballplayer.
Originally an outfielder, Cohen played left field in his major-league debut with the Washington Senators. He made his pitching debut two days later.