Corey Crawford made 18 stops to help Chicago move all alone into fourth place in the Western Conference with 78 points, one ahead of Calgary.
Chicago needed just 55 seconds to score as a turnover by Cory Stillman in his own zone resulted in Toews burying the puck past Peters.
Carolina got the goal back at the 6:23 mark of the first when a rush into the Chicago zone saw Staal trail the play and bury the rebound from the slot for his 29th goal of the season.
However, the Blackhawks took the lead back at the midway mark of the first when Bickell slammed home a rebound off a Brent Seabrook shot for a 2-1 advantage.
After a scoreless second period that saw both goalies make nine saves, the Blackhawks scored three straight in the third to take command of the game.
The first came 2:50 in when Johnson threw the puck to the front of the net from the low left side and it hit off the skate of Joni Pitkanen before trickling past Peters.
Just over a minute later Bolland scored, then Kane made it a 5-1 game at the 7:22 mark on his 22nd goal of the season.
Skinner scored with just under eight minutes to play to account for the final score.
Carolina came into the game having won four of the previous five against Chicago…The Blackhawks hit the road for the next four games starting in Toronto on Saturday…Carolina hosts Atlanta on Wednesday…Both teams went 0- for-2 on the power play.