St. Louis now leads the best-of-7 series, 2-0, needing only two more wins to reach its second World Series in three seasons.
Wacha followed near no-hitters in his regular-season finale and his postseason debut, with an eight strikeout performance in 6 2/3 innings.
Relievers Kevin Siegrist, Randy Choate, Carlos Martinez and Trevor Rosenthal held the Dodgers hitless for the remainder of the game.
Wacha, Siegrist, Martinez and Rosenthal are rookies, and recent players for the Springfield Cardinals.
Game 3 of the NLCS is Monday in Los Angeles.
Dan Lucy will have reaction from the Cardinals clubhouse on Saturday at 10 p.m., on KOLR 10.
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