Bigge earned the save in Friday's 1-0 win over Toronto, striking out two in a perfect ninth inning.
The Rays recalled Bigge from Triple-A Durham on Saturday.
The Rays optioned Bigge to Triple-A Durham on Thursday, Marc Topkin of the Tampa Bay Times reports.
Bigge will serve as the Rays' opening pitcher for Sunday's game in Houston, Marc Topkin of the Tampa Bay Times reports.
The Rays acquired Bigge, Ty Johnson and Christopher Morel from the Cubs in exchange for Isaac Paredes on Sunday, Sahadev Sharma of The Athletic reports.
The Cubs optioned Bigge to Triple-A Iowa on Monday, Ryan Herrera of CHGO Sports reports.
The Cubs recalled Bigge from Triple-A Iowa on Saturday, Andy Martinez of Marquee Sports Network reports.
The Cubs optioned Bigge to Triple-A Iowa on Sunday, Sahadev Sharma of The Athletic reports.