The match had no implications on the MLS postseason race, as both teams have already been eliminated from playoff consideration.
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Austin FC (8-19-4, 28 points) snapped a two-game scoreless streak and won for the third time in its past four home matches.
The expansion side is still in last place in the Western Conference but can achieve a significant milestone over the final three games of its inaugural season. With a victory over FC Dallas next Saturday, Austin would finish with the most points from intra-Texas matches.
Houston (6-14-12, 30 points) remains winless on the road this season (10 losses, six draws). The Dynamo are 1-4-1 over their past six matches and rests in 11th place in the West.
Austin jumped to the lead in the seventh minute in bizarre fashion. Cecilio Dominguez was tripped in the penalty area by Houston's Zarek Valentin and was awarded a penalty kick. But his shot from the spot clanged off the left post before bouncing off Dynamo goalkeeper Marko Maric and just across the goal line.
The home side added to its advantage four minutes into first-half stoppage time as Driussi ripped a shot past Maric from short range upon receiving a nifty pass from team captain Ring.
Austin has been porous in the second half this season, but the defense held fast on Sunday until two minutes into second-half stoppage time. That's when Austin conceded an own goal, when Nick Lima's attempted clearing pass bounced off Julio Cascante and into the net, making the rest of added time a little more nervous for the home side.
Austin's victory allowed it to capture the season series with its Lone Star State rival, with two wins in three matches against the Dynamo.
Austin picks up the 2-1 win over Houston
Austin gets two first-half goals, leading them to a 2-1 win over Houston.