Chivas will face the winner of Wednesday's game between the Seattle Sounders and Los Angeles Galaxy.
Braun scored in the 5th minute when he took a Mariano Trujillo free kick from 40 yards out in the left side of the box and booted it in from six yards. He added another goal in the 90th minute, splitting the Houston defense and hitting a low liner into the left net from 14 yards out.
Michael Lahoud also scored for Chivas in the 65th minute.
Houston's Joseph Ngwenya cut the lead to 2-1 in the 86th minute before Braun's second score.