The game, played at a slow pace on a hot Houston night, looked destined for a stalemate until Colin Clark converted to clinch the points.
Brad Davis had already squandered a penalty well into the second half for Houston, after Chris Schuler shouldered Will Bruin over in the box with the ball several yards away.
But Nick Rimando pulled off an impressive acrobatic save to keep the scoreline square.
Tally Hall showed his own chops at the other end, stopping three shots, including a Ned Grabavoy breakaway.
Three minutes into stoppage time Rimando made the telling mistake, rushing out to punch the ball and taking out Mac Kandji.
Clark then stepped up to smash the ball straight down the middle to win the match.