Wyatt Kalynuk had an assist for his first NHL point, and Lankinen made 27 saves for the Blackhawks (17-16-5), who have lost three of their past four games.
"Tough way to lose, no doubt," Chicago coach Jeremy Colliton said. "It was an up-and-down game, a roller coaster. Would've liked to start better, no question about that. We showed some resiliency to come back a couple of different times, and we had our chances to win it. … It's going to hurt here for a few hours for sure, then we have to find a way to turn the page and start building for Saturday (at the Nashville Predators)."
Trocheck beat Lankinen over his right shoulder with a wrist shot off the crossbar to give Carolina a 1-0 lead at 9:48 of the first period.
Foegele made it 2-0 at 2:22 of the second period when his centering pass from below the goal line redirected in off Blackhawks defenseman Duncan Keith.
"I was just trying to get it to [Nino Niederreiter] there," Foegele said. "Just trying to throw pucks at the net. It's fun how this game works sometimes. There are goals that should go in and some that you get the bounce. Keep it simple, keep playing hard and sometimes you get those bounces."