Williams ran for 101 yards and three touchdowns and threw for a TD for the Tar Heels (9-1, 6-0 Atlantic Coast Conference, No. 23 CFP), who won their ninth straight to stay alone atop the Coastal Division and move within a victory of a berth in the league championship game.
Elijah Hood ran for 132 yards and a score for UNC, which didn't put up the gaudy yardage numbers from last week's 66-31 rout of Duke. But the Tar Heels took advantage of penalties, turnovers and mistakes by the Hurricanes (6-4, 3-3) to turn the game into a romp -- complete with Williams and Switzer commandeering Miami's "The U" hand sign in mocking celebrations of first-half scores.
North Carolina came into Saturday with a chance to qualify for the ACC title game, though that ended when Pittsburgh won at Duke in a game that started 3 1/2 hours earlier.
Now the Tar Heels can earn a date with top-ranked Clemson on Dec. 5 with a win in either of their last two games -- road dates with Virginia Tech and rival North Carolina State -- or a Pittsburgh loss in either of its last two games.
The Tar Heels already have more wins than in any season since Mack Brown left to coach Texas in 1997. UNC is also 6-0 in the ACC for the first time since winning its last ACC crown in 1980.
Brad Kaaya threw for 326 yards and a score for Miami, which lost for the first time in three games under interim coach Larry Scott. Miami was still alive in the Coastal Division but ended up flirting with the worst loss in program history for the second time in four games.
Three weeks after losing 58-0 at home to Clemson in a game that led to the firing of coach Al Golden, the Hurricanes trailed 31-0 at halftime, and then watched the Tar Heels quickly tack on two more touchdowns to make it 45-0 with 10:26 left in the third.
Miami finally scored on Kaaya's 8-yard TD throw to Lawrence Cager with 6:30 left in the third, almost a perfect mirror to last year's meeting when Miami led 44-6 with 7:12 left in the third of a blowout win.
Miami finished with 12 penalties for 103 yards, continuing its trend as one of the nation's most penalized teams. The Hurricanes also committed three first-half turnovers, with the Tar Heels converting two into touchdowns within a span of three snaps and otherwise repeatedly getting short fields for Williams to navigate.
The Tar Heels have a program-record 125 points in the past two games, while Switzer's TD return was the seventh of his career -- one shy of tying the NCAA record.