The sides played out a 0-0 draw in the first leg, leaving the top-seeded Timbers needing any win to set up a Cascadia showdown with the Seattle Sounders.
A goal from Portland's Dairon Asprilla broke the deadlock in the 39th minute, putting the home side in front.
That lead, however, would last less than five minutes.
Dylan Remick's powerful finish put the Dynamo back on even terms in the match and gave them the lead in the tie on away goals.
The crushing blow for the home side came in the 77th minute, when a Mauro Manotas blast found the bottom corner and gave Houston command of the tie.
The win sees the Dynamo move into the conference final, where they will face the second-seeded Sounders, with the first leg slated to take place in Houston after the international break.