McQuinn was a solid-hitting, excellent-fielding, lefthanded first baseman who spent seven years in the Yankee farm system while Lou Gehrig reigned in New York. Drafted by the Browns in 1937, he put together a 34-game hitting streak in 1938, finishing at .324. He remained a St. Louis regular for eight years, leading AL first basemen in fielding three times and in assists twice. In 1944 his opening game home run gave the Browns their first-ever World Series victory.
McQuinn was 4F in the WWII draft because of a bad back, but was reclassified in 1945 when 4F athletes were targeted for service. Through the intervention of Illinois congressman Melvin Price (requested by the Browns) and Happy Chandler, McQuinn and others who were legitimately unable to meet combat requirements were allowed to stay with their teams.
With Gehrig long gone, McQuinn played first base for the Yankees in 1947-48, and was a starting All-Star both seasons. He set All-Star records with 14 putouts and 14 total chances accepted at first base in the 1948 contest. He went on to manage in the minors and scout for the Senators and Expos.