Stanek (1-0) got the win against the Twins on Tuesday, recording a strikeout over a scoreless two-thirds of an inning.
Stanek is the likely option to handle a save opportunity should one arise Sunday in Milwaukee since Andres Munoz is unavailable, Ryan Divish of The Seattle Timesreports.
Stanek was credited with a hold in the win over the Red Sox on Friday, allowing a hit and a walk over two-thirds of a scoreless inning. He struck out one.
Stanek agreed to a contract with the Mariners on Friday, Mark Feinsand of MLB.com reports.
Stanek (personal), who was activated from the paternity list Saturday, made his first appearance of the postseason Sunday in the Astros' 6-2 loss to the Twins in Game 2 of the ALDS, giving up one earned run on two hits over 1.1 innings.
Houston placed Stanek on the paternity list Friday, Chandler Rome of The Athletic reports.
The Astros reinstated Stanek (ankle) from the 15-day injured list Friday.
Stanek (ankle) will begin a rehab assignment Tuesday with Triple-A Sugar Land, Chandler Rome of The Athletic reports.
Stanek (ankle) will throw a bullpen session Wednesday, Chandler Rome of The Athletic reports.
Stanek was placed on the 15-day injured list Tuesday with a right ankle sprain.