Santiago (2-4) yielded two runs on four hits in his second victory in six starts this season, surrendering three walks while striking out six.
Alex Rios socked a solo homer in the eighth for an insurance run and Addison Reed closed out the victory with his 19th save.
Tyler Flowers homered while Conor Gillaspie and Gordon Beckham each provided an RBI as the White Sox earned a four-game split with Oakland.
A.J. Griffin (5-5) was touched for four runs on seven hits over 7 1/3 frames for the Athletics.
Coco Crisp hit a bases-empty home run for Oakland.