Wacha (1-0), who pitched a near-no-hitter in Game 4 of the National League Division Series against Pittsburgh, scattered five hits over 6 2/3 scoreless innings, walking one and striking out eight.
Kevin Siegrist, Randy Choate and Carlos Martinez combined for 1 1/3 shutout relief innings and Trevor Rosenthal struck out the side in the ninth for his first save of the series as the Cardinals shut down the injury-depleted Dodgers line-up.
Kershaw (0-1) allowed just the one unearned run over two hits over six innings, yielding one walk and striking out five.
Los Angeles will host Monday's Game 3.
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