In his ninth career game against New Jersey, Gaudreau scored his first goal against the Devils.
"It's a big win for us, especially where we're at in the standings right now," said Gaudreau, who has put up three goals and four assists in his past four outings.
Before the game, Gaudreau also found out that a goal originally credited to defenceman Michael Stone two nights ago during a 3-2 road win over the Chicago Blackhawks was rightly awarded to him.
Gaudreau's linemate Sean Monahan kept up his recent hot streak by swatting a pair of pucks past Devils goalie Keith Kinkaid to give him goals in four straight games to go with one assist.
"Some good plays out there and we're moving the puck around," said Monahan, who recorded his third straight game-winning marker to give him 10 such goals this season, which leads the NHL. "Luckily enough I got rewarded a couple times."
Goalie David Rittich made 30 saves to improve his record this season to 5-1-2.
"Boy, he's certainly playing well for us," said coach Glen Gulutzan. "He's an extremely hard worker and it translates into the games. He's played some good games, he's made some big saves and he's given us a chance every time he goes in there."
By virtue of their third straight victory, the Flames (28-18-8) moved back into third place in the Pacific Division past the idle Los Angeles Kings (29-19-5) and into a playoff position.
"Two wins to start this road trip, we've just got to build off of that and continue to go," Monahan said.
Taylor Hall had a goal and an assist for the Devils (27-18-8), to extend his point-scoring streak to a career-high 12 games. Pavel Zacha also scored, while Kinkaid finished with 22 saves.
Rittich had to be sharp in the game's first minute to turn aside Blake Coleman's rebound attempt from point-blank range.
The Flames outshot the Devils 12-8 in the opening frame, but weren't able to beat Kinkaid, who denied rookie forward Ryan Lomberg from scoring his first NHL goal in just his second game with six minutes to play before the first intermission.
Monahan opened the scoring at 4:16 of the second when he made no mistake by depositing a rebound into the net behind Kinkaid, who made a shoulder save to stop the initial shot by Dougie Hamilton.
After Hall tied things up by batting his own rebound past Rittich at 7:23, Gaudreau took a breakaway pass from Micheal Ferland and backhanded a shot through Kinkaid's legs at 14:33.
Late in the second stanza, Monahan rang a shot off the post before having the presence of mind to skate around the back of the net to shovel a bouncing puck past Kinkaid.
Zacha pulled New Jersey back within a goal with a power-play goal at 7:23 of the third when he took a pass from Brian Boyle before backhanding a shot past Rittich, who stopped 11 shots in the final frame including one on Boyle with 37.3 seconds remaining and Kinkaid on the bench for an extra attacker.
"I think we were a little too cautious in the third with our game," Gulutzan said. "We let our game slip and they kind of kept pushing us right to the very end."
