Carolina, 3-0-2 in its last five, rebounded from a 4-3 overtime loss Saturday night against Chicago in which it surrendered a pair of two-goal leads. Teravainen notched the natural hat trick in his 212th career game.
Meanwhile, Dallas (9-8) saw its six-game winning streak against Carolina snapped and has now been outscored 22-11 in the third period this season.
Carolina, in a 1-for-29 man-advantage slump, scored its first power-play goal in six games when Teravainen notched his fourth goal of the season 2:39 into the final period to break a 1-1 tie. The left wing then threw what appeared to be a harmless shot toward Ben Bishop four minutes later, but the puck deflected off passing defenseman John Klingberg and past the Dallas goalie.
Teravainen then recorded the team's first hat trick of the season on a shot from the slot for three goals in a span of 7:05.
Jeff Skinner added his team-leading ninth goal with 2.6 seconds left.
Jordan Staal assisted on all but Skinner's goal for the first four-assist game of his 12-year career, while Sebastian Aho broke out of his slump with a goal and two assists.
Aho, who scored 24 goals as a rookie last season for Carolina, notched his first of the season 8:07 into the game after going 15 games without a goal. Aho beat Ben Bishop between the legs after breaking in all alone following a Dallas turnover and defenseman Esa Lindell falling down along the wall trying to defend Staal on a Carolina breakout.
Dallas, with the No. 1 power-play unit in the league, countered with the tying goal midway through the second with the man advantage as Alexander Radulov scored his sixth of the season, extending his point streak to eight games.
NOTES: Carolina came in with the fewest games played (15) in the league. ... Dallas C Tyler Pitlick, who scored two goals against Carolina in a 4-3 Dallas victory on Oct. 21, returned to the lineup after missing two games with an upper body injury. ... Stars G Ben Bishop came into the game 8-1-1 all-time against the Hurricanes. ... Carolina RW Sebastian Aho went his first 14 games last season without a goal. ... Eleven of Carolina's first 16 games have come against the Western Conference. ... The Stars have scored at least one power-play goal in 13 of their 17 games.