He became general manager of the St. Louis Browns from 1917 to 1922, developing the perennially poor team into one which lost the 1922 American League pennant by a single game.

In the summer of 1923, fresh off that success, Quinn put together a syndicate that purchased the Boston Red Sox from Harry Frazee. The purchase was financed by four investors who knew him from his days in Columbus, with the largest contribution coming from glass magnate Palmer Winslow. The investors trusted Quinn enough to make him president and operating head of the franchise. Quinn had every intention of rebuilding a team that had been rendered bereft of talent after Frazee's chronic cash shorts forced him to sell nearly every talented player to the New York Yankees. To that end, he spent $250,000 on minor league stars However, in a case of exceptionally bad timing, Winslow fell ill in 1924 and largely withdrew from financing the team. He died in 1926, and the three surviving members of Quinn's syndicate didn't have nearly enough money between them to make up for the loss of Winslow's investment.

For the remainder of Quinn's tenure as owner of the Red Sox, the team was severely underfinanced. The team lost over $200,000 from 1924 to 1929. This led to a vicious circle in which lack of talent on the field sent attendance through the floor, thus denying Quinn money that could have been used to acquire more players or retain the few good players he had. As a result, Quinn's tenure as owner was, statistically speaking, the darkest in franchise history. With rosters made up mostly of castoffs from other AL teams, they finished finished dead last in the American League eight times during Quinn's ten years as owner, only rising as high as sixth twice. They finally bottomed out in 1932, with a 43–111 (.279) record that is still the worst in franchise history.

By the 1932–33 offseason, Quinn knew he was at the end of his tether. He needed to borrow against his life insurance just to send the team to spring training. Realizing that there was no way he could operate the Red Sox in 1933, he began searching for a buyer. He found his white knight in lumber magnate Tom Yawkey, who had been looking to buy a baseball team as soon as he turned 30 and gained full access to money in a trust fund set up for him by his uncle and adoptive father, former Detroit Tigers owner Bill Yawkey. Former baseball great Eddie Collins, who had attended the same high school as Yawkey, set up a meeting between Yawkey and Collins during the 1932 World Series. The $1.5 million deal closed just before the start of 1933 spring training, and just days after Yawkey turned 30.

Quinn then became general manager of the Brooklyn Dodgers for two seasons (1934–1935) before joining the Boston Braves as team president and part owner from 1936 to 1945. After his 1945 retirement, he briefly served as a sporting goods executive, and then became president of the Baseball Hall of Fame from 1948 to 1951, leaving that position after suffering two strokes.

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