Chicago's Ilya Mikheyev tied the game at 16:48 of the first period with a shot from the left doorstep.
The Blackhawks took the lead at 10:17 when Frank Nazar scored off the rush with a shot from the low slot.
Connor Bedard gave the Blackhawks a 3-1 lead at 11:54 of the third period with a right-circle wrist shot.