The match started at a slow pace but Salt Lake's Fabian Espindola nearly sparked the contest into life with a 40-yard strike that was well saved by Tally Hall.
Houston improved in the latter stages of the first period and could have taken the lead when Ricardo Clark found space inside the box but the defender's shot was blocked on its passage to goal.
Chris Schuler should have put the visitors ahead 10 minutes into the second half but he failed to find the target with his header after losing his marker from a corner.
Houston were handed the opportunity to snatch a victory with 15 minutes remaining when Schuler fouled Will Bruin inside the penalty area.
However, Nick Rimadno denied Brad Davis from 12 yards with a superb save keep the scores level.
As the game looked to be heading for a draw, Rimando quickly turned from hero to villain by giving Houston a second penalty with a foul on Macoumba Kandji.
Clark calmly converted the spot kick to confirm the win for the Dynamo with virtually the last action of the contest.