Nick Cousins scored his first goal, Brandon Montour had three assists, and Eric Staal played his 1,300th NHL game for the Panthers (8-5-1), who have won three of four. The shutout was the first of the season and third in the NHL for Knight, who is 5-1-0.
Antti Raanta made 33 saves for the Hurricanes (8-4-1), who play the Edmonton Oilers on Thursday.
"We're giving up too much," Carolina coach Rod Brind'Amour said. "Especially when you're not scoring, you start doing some things that you shouldn't be doing, and that opens it up the other way. [Raanta] was really good, saved a bunch of odd-man rushes that we were giving up. That's an area of concern. If we don't have 20 guys doing it the right way, it looks like that."
Cousins gave Florida a 1-0 lead at 9:21 of the first period when he tipped Montour's shot from the right point before scoring on the rebound. It was his 11th game since signing a two-year contract July 13.
Aleksander Barkov's power-play goal extended the lead to 2-0 at 10:20 of the third period. He finished a give-and-go with Carter Verhaeghe with a backside tap-in at the left post.
"We have the right mindset, trying to get pucks to the net," Barkov said. "We recognize that they have a really good penalty kill. There's not going to be too many clean plays, so you just have to find your chances and put more pucks to the net and create chances from that."