It looked as if the Union would vault into sole possession of first place in the Eastern Conference as they held a 1-0 lead with time running out.
But Michael Lahoud found Angel undefended at the back post in the 90th minute and the Colombian striker headed a shot off the post and over the goal line, salvaging a point for Chivas (8-12-12).
The Goats remained in seventh place in the West with 36 points on the year.
Justin Mapp scored in the 59th for the Union (10-7-14), who moved into a tie with the Columbus Crew for second place in the East.
Toddler uninjured after being knocked over by Obama family dog
Exploding whale video goes viral on Internet