Alfredsson had two goals and an assist, Helm scored twice and Howard made 29 saves and the Red Wings controlled play for their third win in a row as the Islanders lost their fifth straight.
Since beating Boston 3-1 on home on Nov. 2, New York is 2-10.
"You keep your head up and you keep playing hard but this isn't good enough in any way," Islanders captain John Tavares said. "As a team, all we can think about his playing a better game next time out."
New York came into the game with a 6-0-1 mark against Detroit in its past seven meetings. The Red Wings hadn't beaten the Islanders in regulation since November 2003.
"It's great to see guys scoring goals and gaining confidence," Red Wings coach Mike Babcock said. "And our goaltender had a dominant performance."
The shutout was the second this season for Howard and the 18th of his career.
The 29-year-old goaltender entered with a 0-3-4 record in his past seven starts, allowing at least three goals five times during the streak.
"We were getting chances and burying them," Howard said. "I give all the credit to the team in front of me. We played a very strong game in our zone."
Helm scored his sixth of the season at 7:09 of the first. He took a pass from Alfredsson at the top of the left circle, then skated in and slid a backhand past a flailing Kevin Poulin, making his fifth straight start for the Islanders.
Helm made it 2-0 with a spectacular short-handed score at 16:49 of the second, after he and Poulin lunged for a loose puck in front of the crease.
Helm poked it free and then past the prone goaltender, tumbling upside down to the ice in the process. The goal with Justin Abdelkader in the penalty box brought out boos at Nassau Coliseum.
The 40-year-old Alfredsson, who joined Detroit after 17 seasons with Ottawa, made it 3-0 just 12 seconds into the third, beating Poulin high to the glove side on a breakaway.
"This was a huge win for us," said Alfredsson, who was playing his 1,200th career game and will return to Ottawa on Sunday for the first time.
Alfredsson completed the scoring, knocking a loose puck past Poulin for his sixth of the season and the 432nd goal of his career at 16:13 of the third.
"When you score goals and get great goaltending, you feel better and better as a team," Alfredsson added. "Our hard work going forward will be the key for us."
The 23-year-old Poulin became New York's No. 1 goaltender after starter Evgeni Nabokov was injured when the teams met on Long Island on Nov. 16.
The Islanders won that game in a shootout, but haven't recorded a victory since. Poulin is 2-7 in his past nine appearances.
"Tonight we made decisions with the puck that weren't very good," Islanders coach Jack Capuano said. "You just can't do that against this team or any team."
The Islanders fell to 8-15-3.
The game started slowly with an unusual 4 p.m. start time the day after Thanksgiving. The Islanders outshot the Wings 12-9 in the first period. Detroit had a 9-7 shots advantage in the second.
Detroit's loss on Long Island two weeks ago was part of a stretch when they were 0-2-5 from Nov. 4-19. But the Red Wings have won four of five since, including Wednesday's 6-1 drubbing of Boston at home.
Detroit played without top center Pavel Datsyuk, who was elbowed in the jaw at Ottawa last Saturday and missed his third straight game. Detroit also scratched forward Todd Bertuzzi, out for a fourth straight game with an upper body injury.
Center Josh Bailey was a healthy scratch for the Islanders for the first time this season. Bailey has no goals and two assists since Oct. 25.
The Islanders host Washington on Saturday and Pittsburgh next Tuesday before leaving on a five-game road trip. New York has lost seven straight away from home.
The Islanders continued to be without defensemen Lubomir Visnovsky (concussion) and Brian Strait (upper body). ... New York also scratched left wing Eric Boulton and defenseman Calvin De Haan, who was recalled from AHL Bridgeport on Thursday. ... The Red Wings were also missing defenseman Danny DeKeyser (shoulder). ... The Islanders visit Detroit on Dec. 23.