Garcia (6-7) scattered six hits, didn't issue a walk and struck out five, tossing 60 of his 92 pitches for strikes in the gem. The left-hander allowed only one runner to reach as far as third base.
Mitchell Boggs and Joe Kelly each contributed one scoreless relief frame to complete the shutout for the Cards, who held a 3 1/2-game lead in the National League wild card chase coming into the contest.
Houston's Lucas Harrell (10-11) walked six en route to surrendering a pair of runs on seven hits over five full frames.
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