Tied in the top of the 14th inning, Straw lined a 2-1 pitch from Mariners reliever Matt Festa over right fielder Domingo Santana's head. The ball bounced off the wall and Straw slid into third base as the go-ahead run.
Straw scored on Yuli Gurriel's sacrifice fly later in the inning. Houston held on for the Astros' eighth win in their last 10 games.
"He's the fastest guy we have in our organization and our team," Astros manager AJ Hinch said. "Usually, at any field that he's at, he's going to be the fastest guy."
MLB Statcast measured Straw's sprint speed as the Astros' fastest triple since Statcast tracking began in 2015.
Straw was recalled from Triple-A Round Rock last week when shortstop Carlos Correa was placed on the injured list with a fractured rib. Straw is hitting .333 with an RBI and seven runs scored in 18 at-bats this season.
Straw, 24, has also stolen three bases in his short time with the Astros.
"One of the reasons we love him so much is the pressure that he puts on with his legs," Hinch said. "When he adds the bat to it, he's a really good player."
Houston moved to 43-21 with Thursday's victory. The Astros have a nine-game lead over the Texas Rangers for first place in the AL West Division.