Kozma became the Cardinals' primary shortstop in 2013 and finished with a .217 batting average, 20 doubles, a home run and three stolen bases in 143 games. They secured the best record in the National League, thus making the playoffs. He provided a key defensive play in the sixth inning of Game 3 of the NLCS against the Los Angeles Dodgers. Dodgers batter Juan Uribe hit a rapid ground ball in the hole, which Kozma backhanded and relayed to second baseman Matt Carpenter, tipping off an inning ending double play. The Cardinals won the game, 4–2.