Shea, who signed a four-year contract extension this week, scored first, finishing up a cross into the 6-yard box from Castillo in the 29th minute.
Castillo made it 2-0 in the 43rd with his second goal of the year off a cross from Jackson Goncalves at the edge of the 6-yard box that beat goalie Faryd Mondragon.
Goalie Kevin Hartman posted his third straight shutout for FC Dallas (5-3-2), which extended its unbeaten streak to five games -- four of which have been wins.
Philadelphia, meanwhile, fell to 4-3-2.
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