Jacobs and Miguel Olivo hit back-to-back homers in the fourth inning.
Winner Zack Greinke (11-7) gave up three early runs before settling down. The right-hander, who ended a six-start winless stretch, scattered seven hits and two walks in seven innings.
Alberto Callaspo went 3-for-4 with two RBI, and David DeJesus had two RBI for Kansas City.
Clay Mortensen (0-1), making his first major league start, surrendered eight runs on eight hits and three walks in four-plus innings for the Athletics. Mark Ellis went 2-for-4 with a home run and three RBI for Oakland.