Morales put RSL ahead to stay in the 39th minute, beating Dallas defender Zach Loyd in a one-on-one battle with a quick shot.
The score remained 1-0 until the 79th minute, when Morales started a play that resulted in Ned Grababoy scoring off a crossing pass from Kenny Mansally.
Morales figured again on an Olmes Garcia tally in the 90th minute as RSL (11-5-4) tightened its grip on first place in Western Conference with its first-even win in Texas.
Dallas, which came into the contest holding the West's second spot, fell to 8-5-7.
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