Ross (6-0) was forced into action after Ogando exited with a strained groin following three scoreless innings to start the game.
The American League hurler was hurt while running to first during a fourth-inning at-bat necessitated by the National League rules in force at AT&T Park.
Ross, however, responded by limiting the Giants to one hit over four frames, issuing no walks and striking out two. Mike Adams followed with a scoreless eighth and Joe Nathan completed the shutout for American League West-leading Texas.
Giants starter Tim Lincecum (2-7) turned in his eighth straight start without a win, surrendering five runs on nine hits over 5 2/3 innings.