It only took 16 minutes for the Dynamo to open the scoring with Will Bruin running on to Ricardo Clark's perfectly executed back-heel and curling the finish past Impact goalkeeper Troy Perkins.
The Dynamo made it two 11 minutes later after Boniek Garcia converted from the spot after being brought down by Montreal defender Hernan Bernardello in the area.
Houston custodian Tally Hall made several saves throughout the rest of the first half and early in the second, denying Italian veteran Marco Di Vaio twice before saving Justin Mapp's header.
Things went from bad to worse for the Impact on 70 minutes with defender Nelson Rivas shown a second yellow card for an elbow on Bruin.
Two minutes later, Bruin made the most of the advantage, finding space at the back after outpacing Mateo Ferrari and finishing cleverly past the onrushing Perkins to make it 3-0.
Incredibly, Montreal was reduced to eight men in the 89th minute after Andres Romero was sent off for kicking out at an opponent and Di Vaio was dismissed for fighting in the aftermath.
Houston now advances to the Eastern Conference semi-final against New York Red Bulls with the two legs to be played on November 4 and 7.
