Even if they win their final six games, they still face long odds in qualifying, but on this day they remained alive.
"Getting three points when our backs are against the wall [is big]," said Union team manager John Hackworth.
Adu broke a 1-1 deadlock by converting a penalty kick in the 50th minute. Teammate Sheanon Williams earned the penalty kick when he was taken down inside the box.
Adu hurt his hip taking the penalty kick and left the game a few minutes later. He said he hopes to play in the next game, Saturday at Columbus, but it's too early to tell.
"Somehow we are still in it, and we will keep fighting, and you never know what will happen," said Adu, who has five goals.
The Union increased the lead to 3-1 when Josue Martinez, standing at the far post, tipped in a shot by teammate Amobi Okugo in the 70th minute. It was Martinez's first career MLS goal.
"I am very excited, and it was a great feeling getting that first goal," Martinez said through an interpreter.
Martinez had other chances, including in the 11th minute when he was stoned by keeper Tally Hall from close range.
Adu scored the game's first goal in the 28th minute, thanks to some great work by rookie defender Ray Gaddis, who carried the ball deep into the Houston defensive zone. Gaddis sent a ball that Adu saved from going out of bounds.
Adu then bought himself some space by faking a shot, forcing defender Kofi Sarkodie to back off. Then Adu, from just beyond the six-yard line, shot it inside the near post.
Houston didn't mount much of an attack until late in the first half, when the Dynamo's Boniek Garcia got the equalizer in the 44th minute.
Taking a pass from Will Bruin, Garcia blasted a one-timer from 12 yards out at an angle on the right side. The ball hit the far post and bounced in. This came after Garcia was stoned by Zac MacMath in the 42d minute.
"We played really well for 42-43 minutes, and I told them we had to come back in the second half and bring it," Hackworth said.
And the team did exactly that, keeping its slim playoff hopes alive as well.
Contact Marc Narducci at firstname.lastname@example.org, or follow on Twitter @sjnard.