Australia international Garcia struck three minutes into added time of the final regular-season game of the campaign to earn a home win that ensured Sydney finished fifth.
Frank Farina's men finished the season in fifth and will now face rivals Melbourne Victory, as opposed to reigning champions Central Coast Mariners, who they were on course to meet before Garcia's late intervention.
Terry Antonis' superb long-range strike gave the hosts the lead seven minutes minutes before half-time at the Allianz Stadium.
However, Rostyn Griffiths' second A-League goal of the season deservedly drew the Glory level in first-half stoppage time.
A nervy second period ensued, but Garcia settled matters in the final seconds when he latched onto Alessandro Del Piero's superb, lofted throughball and beat Glory keeper Jack Duncan.
The result ended the Glory's mini-revival - which had seen them win their last two league games - and means they finish the season in eighth place.
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