Los Angeles won for the eighth time in nine games when the Cardinals' Edward Mujica suffered his first blown save of the season in 22 chances.
Mujica (0-1) retired the next two batters to give the Cardinals a chance to get into extra innings, but Aybar singled to center on a 2-1 pitch to bring home Kendrick.
The comeback made a winner out of Scott Downs (2-2), who worked the top of the ninth.
Allen Craig hit a three-run homer in the fourth for the Cardinals.
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