The Dynamo, which hadn't beaten the Fire since 2010, advances to host top-seeded Kansas City in Sunday's first leg of the Eastern Conference semifinals.
Houston had to hold off Chicago in the last seven minutes. Brazilian veteran Alex beat Dynamo goalkeeper Tally Hall with a low right-footed shot in the 82nd minute, cutting Houston's lead.
Bruin, a first-round pick in the 2011 draft, headed in a corner kick for his first goal. Midfielder Brad Davis' cross from the left side was perfect, with Bruin's header bouncing off the turf before bounding by Chicago goalkeeper Sean Johnson in the 12th minute.
Houston took advantage of a Chicago mistake at the start of the second half for its second goal. Fire defender Gonzalo Segares' clearing pass was deflected. Oscar Boniek Garcia led Bruin. Johnson got his right hand on Bruin's 10-yard shot, but couldn't stop it 19 seconds into the second half.
Houston controlled the ball more effectively for the first 75 minutes, giving Hall an easy night until Alex's goal.
Chicago's best chance before the goal, a point-blank drive by forward Sherjill MacDonald, was kicked aside by midfielder Adam Moffat in the 71st minute.
Notes: Houston is 1-0-2 against Kansas City this season. ... The second leg of the semifinals is Nov. 7 in Kansas City. ... Houston was undefeated (11-0-6) at home this season, a 29-game unbeaten streak dating to July 9, 2011, including last year's playoff matches en route to the Eastern Conference title. ... The Dynamo last beat the Fire on Aug. 21, 2010, in a regular-season match.