Sebastian Aho had a goal and an assist, Andrei Svechnikov and Tony DeAngelo each had two assists, and Alex Lyon made 27 saves in his debut with the Hurricanes (11-2-0).
Smith took a cross-ice pass from DeAngelo inside the blue line and scored on a slap shot for his first goal in his fourth game with Carolina.
"[DeAngelo's] passes are so perfect. They're right on your tape, but they're putting you in a position to make a play," Smith said. "I was able to walk into a slap shot. We had a good screen in front. I'm obviously very excited. It's a moment I'm never going to forget."
Lyon signed with the Hurricanes as a free agent July 30 and was recalled from Chicago of the American Hockey League on Nov. 7. It was the 23rd NHL game for the 28-year-old.
"Coming up to the NHL is something I've battled for a long time, just trying to find my way," Lyon said. "Hopefully I'm good enough to be up here. I feel like every time I play up here, it gets a little easier."
Pavel Buchnevich and Vladimir Tarasenko scored, and Robert Thomas had two assists for the Blues (8-3-2). Joel Hofer made 21 saves in his second NHL start.
"It was a good game, a tight game, but you hate giving up that goal late in the third period like that," St. Louis coach Craig Berube said. "I thought the second half of the game, we looked really good. In the end, you've got to find a way to get three goals."