Kozma was optioned to Triple-A to begin the 2012 season. He was recalled to the Cardinals on August 31, 2012, when Rafael Furcal was placed on the disabled list. Kozma singled to give the Cardinals the deciding runs in the winner-take-all fifth game of the 2012 National League Division Series (NLDS) over the Washington Nationals. During the NLDS, he hit a home run—his first in an MLB postseason—and drove in five runners. Kozma batted .227 during the NLCS against the San Francisco Giants and added a stolen base. Despite attaining a 3-games-to-1 advantage in the series, the Cardinals lost the Series in the 7th and deciding game.