The Panthers (11-3) own a two-game lead in the NFC South over Tampa Bay and Atlanta with two games remaining. A loss by Dallas to the New York Giants Sunday night would clinch a post-season spot for Carolina.
Denver (8-6) missed out on a chance to wrap up the AFC West title. The Broncos need one win in the last two weeks or a loss by San Diego to clinch the division crown.
The Broncos took a 10-7 lead late in the first period but did not score another point. Carolina tied the game on the first of three field goals by John Kasay, and then moved in front when Jonathan Stewart scored on a 2-yard run midway through the second period.
Kasay made it 20-10 at halftime on a 44-yard kick and Williams broke things open early in the second half with his long scoring run. Williams gained 88 yards on 12 carries and Carolina quarterback Jake Delhomme threw for 253 yards and a score.
It was Carolina's third straight win and the Panthers completed a four-game sweep this season of teams from the AFC West.