Kelly's first MLB postseason series was the 2012 National League Division Series, against the Washington Nationals. He appeared in three games and pitched innings of relief without giving up a run or a hit; he walked one batter and struck out three batters. The Cardinals then advanced to the 2012 NLCS against the San Francisco Giants. In the deciding Game 7, Kelly came on to pitch in the third inning with the Giants ahead 2–0 with the bases loaded and no outs; he gave up two hits and two walks, lasting just of an inning, and exited with the Giants ahead 7–0, in a game they would go on to win 9–0. Overall, Kelly made four appearances in the series, pitching a total of four innings in relief; he gave up six hits and was charged with two earned runs, while walking three batters and striking out two batters.