Bobby Farnham and Kyle Palmieri also scored for New Jersey, and Keith Kinkaid stopped 26 shots.
Eric Staal scored twice and Kris Versteeg had two assists for the Hurricanes. Cam Ward made 21 saves.
Carolina trails the New York Rangers by nine points for third place in the Metropolitan Division.
With the score tied 2-all, Schlemko fired a shot from the half wall that eluded Ward for the go-ahead goal.
Staal opened the scoring 2:51 into the second period with his sixth of the season. Farnham, just activated from injured reserve, tied it at 6:06 with his fourth in 20 games.
Staal scored his second of the period at 9:46. He began the sequence by forcing Andy Greene's turnover along the half wall. Versteeg won a board battle, leading to Staal tucking a shot from behind the goal line past Kinkaid.
Palmieri tied it at 7:14 of the third by tipping Jon Merrill's point shot past Ward. Carolina coach Bill Peters used his coach's challenge, but the ruling was upheld. Replays showed Palmieri did not make contact with Ward as he stood at the top of the crease.
Carolina and New Jersey played for the second time in three days, and the third time in December. The teams will play twice more this season, March 1 in Newark and March 27 in Raleigh, North Carolina.
NOTES: Before the game, New Jersey announced Patrik Elias had been placed on injured reserve, retroactive to Dec. 21, with a knee injury. Elias, the club's career leader in goals (407), assists (615), points (1,022), power-play goals (113) and game-winning goals (80), has one goal and four assists in 13 games this season. He needs to play in 47 more games to pass Ken Daneyko to become the Devils' all-time leader in games played with 1,284. . Carolina scratched Michal Jordan and Brad Malone. ... Eric Gelinas and Jacob Josefson were scratched by the Devils. New Jersey wing Tuomo Ruutu missed the game due to illness.