After Vancouver's Jun Marques Davidson scored an own-goal in the 12th minute for a 1-0 Goats lead, Avila doubled the advantage in the 55th on a right-footed volley.
Chivas (3-1-1) went on to earn a point for a fourth straight game, good for second place in the Western Conference.
Kenny Miller made it close with a score in the 64th for the Whitecaps (2-2-0).
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