With the score knotted at 1-1 in the 71st minute, Brian Ching led a break and found Garcia, who curled a shot past Union goalkeeper Zac MacMath and into the net for the game-winner.
Davis added a penalty kick in the 75th after Will Bruin was taken down by Carlos Valdes in the box, and the Dynamo (14-8-11) made the post-season for the sixth time in seven years.
Macoumba Kandji scored early in Houston's victory.
Jack McInerney got the only goal for Philadelphia (10-16-6).
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