Santana (9-12) had won only one of his previous four starts, but dominated Chicago in handing the White Sox their third straight setback.
Chicago's lead in the American League Central was reduced to 1 1/2 games over Detroit, which had its scheduled meeting with Minnesota rained out.
Los Angeles tied it in the second on a solo homer by Kendrys Morales and Albert Pujols put the Angels in front in the third with a two-run single.
Torii Hunter added a two-run base hit in the fourth and Mike Trout tacked on a solo homer in the seventh to give Los Angeles a 6-1 lead.
Jake Peavy (11-12) suffered the loss, surrendering five runs on eight hits in five innings.