The win earned Houston a 3-1 aggregate victory and allowed them to reach their fourth conference final in the past six years. They will play Sporting Kansas City in Sunday's game with the winner going through to the MLS Cup on November 20.
The game was a scrappy encounter played on a poor surface in what was Dynamo's last game at Robertson Stadium before they move to their new, purpose-built new soccer stadium in downtown Houston next season.
The Western Conference final will be between Real Salt Lake and the winner of Thursday's game between L.A Galaxy and New York Red Bulls. Galaxy lead 1-0 from the first leg.
(Reporting by Simon Evans in Miami; Editing by Nick Mulvenney;
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