One of two hits for Branyan was a two-run sixth-inning homer and one of two hits for Gutierrez was a two-run ninth-inning double.
Endy Chavez had two hits and one RBI.
Yuniesky Betancourt had one RBI, while Ichiro Suzuki had three hits for the Mariners, who averted a three-game sweep.
Winner Erik Bedard (3-2) surrendered an earned run and five hits in 6 2/3 innings with two walks and five strikeouts.
Bobby Crosby's second-inning homer, his first this season, produced Oakland's only run.
Jack Hannahan and Matt Holliday had two hits apiece for the Athletics, whose three-game winning streak ended.
Losing pitcher Trevor Cahill (2-5) yielded three runs – two earned – and six hits in six innings with one walk and five strikeouts.
Oakland failed to record its first three-game sweep this season.
Celebrity Breakups and divorces of 2014 [PHOTOS]