Bruney was 5-0 with a 3.92 ERA in 44 regular-season appearances. He was not active for the first two rounds of the playoffs and has not pitched in a game since Oct. 2.
Hinske, acquired from Pittsburgh on June 30, was on the roster for the AL Division Series against Minnesota but did not appear.
Hinske pinch hit for Tampa Bay in Game 4 of last year's World Series and homered off the Phillies' Joe Blanton. He also pinch hit in Game 5, striking out against Brad Lidge with a runner on second for the final out in Philadelphia's 4-3 win, which completed a five-game Series victory.