Wallmark gave Carolina a 1-0 lead at 10:47 of the first period with a shot from above the face-off circles.
It was the first time in six games the Hurricanes scored the first goal.
"We've been struggling to score," Martinook said. "Sometimes you need that ... not sure it's a good shot, it's from far out and sometimes you need one to get you jump-started, and hopefully that's the one that can get us going."
After Martinook scored, Svechnikov made it 3-0 at 2:19 of the second with a shot from between the top of the circles. It was his 11th goal, second among NHL rookies after Vancouver Canucks forward Elias Pettersson's 19.
Hart, a rookie making his fifth start since being recalled from Lehigh Valley of the American Hockey League on Dec. 17, has lost three straight after winning his first two NHL games.
"Just three pucks that I should have," he said. "Going forward, I'll learn from it. Put it behind me and move on to the next one, that's the name of the game. There's going to be nights that don't go our way; tonight was one of those nights."