"He was all over the net," Tavares said about Moulson. "He probably could have had six or seven. He was on fire."
Moulson scored twice in the wild, seven-goal second period, giving the Islanders a 5-4 edge off a 3-on-2 break with 2:50 left with his team-high 13th goal of the season.
Moulson also missed on a breakaway and had several other scoring chances, finishing with seven shots on goal and three others that missed the net.
He was eager to credit the setup work by Tavares and Parenteau.
"They really gave me some good chances, all I had to do was sweep it into an open net," Moulson said. "The win's the biggest part. Score as many goals as you want, but the win's the most important thing."
Moulson is the first Islanders player to score four goals since Viktor Kozlov against the Rangers at Madison Square Garden exactly five years ago - Dec. 3, 2006. The Islanders' record is five, set by Bryan Trottier in 1978 against the Rangers and matched by John Tonelli in 1981 against Toronto and Trottier in 1982 against Philadelphia.
Dylan Reese added his first goal of the season for the Islanders.
Eric Nystrom, the son of former Islanders great Bobby Nystrom, connected for Dallas, giving him 10 goals in his last 16 games. Tomas Vincour, Jake Dowell and Tom Wandell had their first goals of the season for the Stars.
Moulson shoveled a power-play rebound of Taveras' shot past goalie Andrew Raycroft at 8:55 of the opening period, then gave New York a two-goal pad at 10:54 of the first period after the puck bounced off the end boards on a shot by Tavares and onto Moulson's stick.
Reese made it 3-0 at 2:48 of the second period on a shot-pass from center point that fluttered past Raycroft's glove.
Dallas rallied with three goals in a 2:03 span to draw even.
"We have some resiliency, I don't think that's going to change for us," Stars coach Glen Gulutzan said. "However, we can't keep battling back every night. We've got to play with a little sense of urgency at home and make sure our first periods are better."
Vincour's deflection at 3:27 got the Stars on the board, and Nystrom struck from in front of the net at 4:53 to make it a one-goal game.
Dowell tied it at 5:30, but Moulson completed his hat trick 27 seconds later to put the Islanders back in front.
Wandell beat DiPietro with a 40-foot slap shot with 3:52 to go in the period to square the score at 4.
The Isles began the night averaging 2.04 goals, last in the NHL. New York had been shut out three times in its previous seven games. But the Islanders, coming off Friday night's 5-4 shootout loss at Chicago, have picked up the pace with nine goals in their last two games.
The Islanders went 3-0-1 on a four-game trip that concluded in Dallas, where the Stars had been 9-3-1.
"It wasn't the prettiest, but we got three of four points in these last two games," Tavares said.
- A Dallas opponent hadn't scored four goals in a game since Keith Tkachuk for Winnipeg on March 26, 1996, an 8-2 loss for the Stars.
- Raycroft made his third consecutive start while regular Kari Lehtonen recovers from a groin injury.
- Out for the Stars were LW Brenden Morrow [multiple injuries], D Alex Goligoski [broken thumb], D Trevor Daley (back) and forward Adam Burish [broken hand].
- Dallas was 13-4-1 in its previous 18 games against the Islanders.
- G Evgeni Nabokov (groin), D Mark Eaton (knee), D Andrew McDonald (leg) and RW Jay Pandolfo (foot) were out for the Isles.