Houston won on the road just three times in 17 attempts during the regular season, but pulled off the upset away from home against the Fire to move into the Eastern Conference semifinals.
The Dynamo will now take on Kansas City in a two-match, aggregate-score series with Houston hosting the first game next Sunday. The second game will be played in Kansas City on Nov. 7.
Bruin opened the scoring in the 12th minute, sending a header past goalkeeper Sean Johnson off a pass from Brad Davis.
The other goal from Bruin came in the opening minute of the second half. He sent a shot across the face of the goal and into the left corner of the net.
Chicago scored in the 83rd minute.
Los Angeles will host Vancouver on Thursday in a Western Conference matchup with the winner moving on to meet San Jose, which had the league's best regular-season record.