Chicago took a 4-0 lead into the seventh before starter Philip Humber ran into trouble. He allowed two runs and had the bases loaded with nobody out when Jesse Crain came in to start the outstanding effort by the bullpen.
Crain escaped the trouble by giving up only a sacrifice fly that cut the A's deficit to one. Crain also retired the first batter in the eighth before Matt Thornton finished off the inning and Santos struck out two during a 1-2-3 ninth for his fourth save.
All of Chicago's runs came in the second, which was highlighted by an RBI double from Omar Vizquel.
Vizquel eventually scored an unearned run, which turned out to be the game-winner, when starting Oakland pitcher Brandon McCarthy threw wildly to first base on a pickoff attempt.
Humber (3-3) did not walk a batter and struck out one while picking up the win.
McCarthy (1-4) allowed four runs, three earned, on five hits in seven innings.