The yardage total was a Panthers' franchise record.
Overall, Williams, in his third season out of Memphis, gained 186 yards on 19 carries.
He had three runs of at least 35 yards against the NFC's No. 2 ranked defense, including a 36-yard, fourth-quarter touchdown.
His effort helped Carolina rush for a team-record 299 yards and first place in the NFC South Division.
Joining Williams in earning the NFC's weekly awards were Arizona Cardinals linebacker Gerald Hayes (defense) and New Orleans kick returner Pierre Thomas (special teams).
Hayes, in his sixth year from Pittsburgh, made a team-high 12 tackles, one-half sack and forced two fumbles in the Cardinals' 34-10 win over the St. Louis Rams.
Thomas had 197 all-purpose yards, two touchdowns and set up the game-winning score with an 88-yard kickoff return in the Saints' 29-25 victory against the Atlanta Falcons.