Succop's five field goals were a career high and his 54-yarder was his longest as a pro.
Matt Cassel gained 260 yards and hurled a TD pass to Dwayne Bowe for the Chiefs (1-3), who avoided an 0-4 start with the victory.
Bowe finished with five catches for 107 yards and Steve Breaston added four catches for 91 yards.
Minnesota, meanwhile, fell to 0-4 for the first time since 2002.
They lost despite Donovan McNabb's 18-of-30 passing performance for 202 yards, two touchdowns and one interception.
Adrian Peterson amassed 80 yards on 23 carries for the Vikings.