Erik Haula scored, and Juuse Saros made 25 saves for the Predators (24-20-1), who are 0-4-1 against the Hurricanes this season and remained four points ahead of the Chicago Blackhawks for fourth place in the division.
"They put a lot of pressure on you and go right at you," Haula said. "Puck management is key against them. In the second period, we got away from that. It was kind of a collective effort."
Carolina took a 1-0 lead at 18:26 of the first period when Jordan Staal chased down a long clearing attempt by Mrazek and sent a centering pass to Foegele, who scored with a backhand at the top of the crease.
"I thought I had a step on my guy and was hoping [Staal] saw me," Foegele said. "Just a beautiful pass by him. I was happy to get that one in."
Svechnikov scored 14 seconds into the second period during a 4-on-4 to put the Hurricanes ahead 2-0. He took a pass from Dougie Hamilton just inside the blue line and split Predators defenseman Roman Josi and Ryan Ellis before beating Saros under his right arm with a backhand.
It was Svechnikov's first goal since March 30 and his second in 12 games.
"Obviously, when you score a goal you feel more confident," he said. "But it's just one goal, so I've got to keep going."