MLS: Chicago 1 Houston 2
The Dynamo striker scored a goal in each half to hand Houston a 2-0 lead at Toyota Park before Alex pulled a goal back seven minutes from full-time to make it 2-1.
The Fire started tentatively with goalkeeper Sean Johnson mishandling a couple of early balls before letting Bruin's header dribble in on 12 minutes.
The Fire lifted the tempo and managed several efforts on goal but it was Houston who went further ahead when Bruin grabbed a second from Calen Carr's delivery shortly after the break.
Chicago continued to press but only managed to pull one goal back in the second half through substitute Alex's deflected strike off the post.
An MLS Cup finalist in 2011, the Dynamo now advance to the conference's semi-finals on Sunday against top seed Kansas City.