Photo credit: Christian Bonin/Toronto Marlies
Ben Smith scored into an empty net at 18:29 to make it 5-1, and Marchment made it 6-1 with his second of the night at 19:04.
Mike McKenna made 40 saves for Texas, which won the Calder Cup in 2014.
The Stars forced Game 7 with a 5-2 win in Game 6 on Tuesday.
"I felt a personal responsibility to step up (after Game 6), and I thought I did that," Sparks said. "... Good guys in the room, amazing talent, great leadership on and off the ice, incredible management, incredible training staff. All of the factors that I listed played a role in this."
It was the first Game 7 in the AHL championship series since 2003, when Houston defeated Hamilton 3-0, and the 11th in league history.