Reto Ziegler and Jesus Ferreira also scored goals, and Jesse Gonzalez had three saves for FC Dallas (11-10-7, 40 points), which leapfrogged the Portland Timbers (11-11-4, 37) into seventh place and the final playoff spot in the Western Conference.
The Toros also retained possession of "El Capitan" -- a trophy replica of an 18th century cannon that goes to the team with the best head-to-head record in the rivalry -- due to goal differential. Houston had won the first meeting, 2-1, at home on May 4.
FC Dallas took a 1-0 lead in the 24th minute on Ziegler's left-footed penalty kick into the right corner. The goal was set up when Houston defender Jose Bizama took down Dominique Badji inside the box.
Ferreira made it 2-0 just five minutes later when he took a pass from Ondrasek at midfield, dribbled down the middle of the field and then deked defender Aljaz Struna at the top of the penalty box before firing a right-footed shot into the right corner for his team-leading seventh goal of the season.
Ondrasek scored twice in an eight-minute span early in the second half to increase the FC Dallas lead to 4-0. The first came off a cross from the left side by Ryan Hollingshead to Ondrasek, who made a direct run near the far right post and redirected the ball with his right leg into the net. The second came off another crossing pass from the left side of the box by Badji that a sliding Ondrasek deflected past Willis.
Rodriguez put Houston on the board in the 80th minute with his sixth goal of the season, off a pass from Mauro Manotas following a FC Dallas turnover in the box.
Barrios made it 5-1 in the sixth minute of stoppage time when he picked up a loose ball in front of the 6-yard box and rifled a shot past Willis for his third goal of the season.