Cobb (10-3) yielded just one run on five hits over 8 1/3 innings, striking out 12 and walking two. He improved to 4-1 in eight starts since his Aug. 15 return from an injury.
The victory was a crucial one for the Rays, who outlasted Baltimore 5-4 in 18 innings Friday to grab a one-half game lead over Cleveland for the first American League wild-card spot with nine contests remaining.
Miguel Gonzalez (10-8) allowed three runs, walking five while allowing two hits for Baltimore, which fell three games off the wild-card pace.
Adam Jones provided the Orioles' only RBI.