Jones' 1-yard TD plunge with 10:14 remaining in the second quarter put the Chiefs up 14-3 and his 3-yard scoring run five minutes into the second half gave Kansas City (6-4) a 21-3 advantage.
Jones gained 71 yards on 15 carries, Dwayne Bowe made six catches for 109 yards with a pair of scores and Jamaal Charles added 88 yards on 12 carries in the win.
Kansas City's Matt Cassel connected on 15-of-24 pass attempts for 193 yards and two TDs to Bowe for Kansas City, which took a one-game lead over Oakland atop the AFC West.
The Cardinals (3-7) lost for the fifth straight time. They were led by Derek Anderson, who went 25-for-46 passing for 295 yards and a score.
Tim Hightower rushed for 62 yards for Arizona.