Newton made good on 16-of-24 throws for 273 yards with a 72-yard touchdown pass to Williams as the Panthers (10-4) rebounded from last week's loss to New Orleans for a ninth win in 10 games.
Williams caught three passes for 87 yards and carried the ball 15 times for 81 more.
Captain Munnerlyn recorded a pair of sacks and returned an interception for a touchdown for Carolina, which could clinch a playoff spot next week in its second meeting with the Saints.
Geno Smith completed 15-of-28 for just 167 yards with a TD and an interception for the Jets (6-8).
Jeff Cumberland made three grabs for 50 yards and a score.