Brian Ching's headed goal just before the half gave the Dynamo a two-goal aggregate lead that effectively killed off the tie.
"We wanted to win, to close it out, but more importantly we wanted to continue our playoff run," Corey Ashe told Goal.com. "The goal is to bring back another MLS Cup, and that's what we're trying to do."
Philadelphia surprisingly started with Jack McInerney and Danny Mwanga paired at forward with Sebastien Le Toux slotted into a midfield role. The move didn't provide much spark for the visitors in the first half, as they were reduced to playing long balls over the top that rarely led to good chances.
Houston had several set-piece opportunities throughout the first half, but the Union defended the service from Brad Davis much more effectively than they did in the first leg.
However, the Philadelphia's resistance broke right before the half. Just as it looked like the match was heading into the break scoreless, Ching popped up with a crucial goal.
Carlos Valdes conceded a free-kick 40 yards from goal, and Brad Davis curled in a great cross which Ching rose up and nodded past Faryd Mondragon. The goal gave Houston a 1-0 lead on the night and a 3-1 aggregate advantage.
"They've been in the league for a while," Ashe said, exclusively to Goal.com. "They've been on the team since it was in San Jose. These guys are leaders. For them to do that, it speaks volumes about their heritage. We needed both of them to step up and they stepped up."
Mondragon made a big save 10 minutes into the second half to keep his side in the tie after Calen Carr got on the end of a long ball and behind the Union defense.
With 20 minutes left, Union coach Peter Nowak made one last throw of the dice with a triple sub, introducing Freddy Adu, Justin Mapp and Roger Torres. It wasn't enough, though, and Houston saw out the match comfortably.
The Dynamo will face Sporting Kansas City on Sunday in the Eastern Conference final.
Allen Ramsey contributed reporting to this article.
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