Williams scored three touchdowns in the first half -- two on the ground and on a pass -- when Carolina built a 21-0 halftime advantage. He finished the contest with a career-high 123 yards rushing on 20 carries.
Quarterback Jake Delhomme completed 14- of-22 passes for 236 yards, two touchdowns and one interception.
Steve Smith caught six passes for 96 yards and Jonathan Stewart rushed for 72 yards on 19 carries for the Panthers (4-1).
Kansas City quarterback Damon Huard was held to 10-of-21 completions for 86 yards and two interceptions.
Star running back Larry Johnson rushed for only two yards on seven carries, and wide receiver Dwayne Bowe caught five passes for 57 yards for the Chiefs (1-4).