Stirnweiss was in three World Series and appeared in the All-Star Game in 1945 and 1946. He won the American League batting title in 1945 with a .309 average. On the final day of the season, he trailed Tony Cuccinello, whose final game had been rained out. After Stirnweiss singled in his first two at-bats, word came from the press box that he was ahead of Cuccinello and should sit out the rest of the game. He refused to do so, but then went out his next two times up. In the final inning, he singled. Without the additional 1-for-3, he would not have beaten Cuccinello. However, this fact was never discussed in the press.
A prolific base-stealer, he led the AL with 55 stolen bases in 1944 and with 33 in 1945. In the same period, he also led the league in runs (125 and 107), hits (205 and 195), triples (16 and 22), and in fielding percentage. In 1948, with only five errors tallied against him, Stirnweiss set a major league record for a second baseman with a .993 percentage.
The Yankees traded Stirnweiss to the St. Louis Browns in 1950 and the next year he was sold to the Cleveland Indians. He retired after the 1952 season. Following his retirement as a player, he managed in the minor leagues, and later entered the banking field.