Kennedy had to move quickly to turn aside Shea's volley off a cross from Andrew Jacobson down the stretch.
He also made a scrambling, finger-tip stop on a Jackson try in the first half for Chivas USA (5-7-4).
The draw allowed the Goats to move into a tie for the fifth playoff spot in the Western Conference.
Kevin Hartman, meanwhile, needed to make only one save for Dallas (3-9-4).
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