Anor was in the right position from 1 yard out to finish Tony Tchani's deflected shot.
The Crew (14-10-10) can still earn the No. 3 seed and a knockout-round bye pending the result of Sporting Kansas City's home match with the New York Red Bulls on Sunday night.
If Sporting KC wins, the Crew will host the Red Bulls in the knockout match on Thursday. If Sporting KC ties or loses to the Red Bulls, the Crew will advance directly to the Eastern Conference semifinals.
Zach Pfeffer tied the game for the Union (10-12-12) in the 85th minute with his first career MLS goal.
Jairo Arrieta opened the scoring for the Crew with a breakaway goal in the 13th minute.