Helm scored the game's first two goals, Alfredsson added two in the third period, and Howard stopped all 29 shots he faced in a 5-0 victory Friday at Nassau Coliseum.
It was the Red Wings' first victory against the Islanders since Jan. 30, 2007, and their first in regulation since a 6-0 win on Nov. 28, 2003. New York had been 6-0-1 in the past seven games between the teams.
The Red Wings played their puck-possession style perfectly, and the Islanders struggled with their decision-making.
"You saw our execution tonight," coach Jack Capuano said. "We made some decisions with the puck that weren't very good. We can't do that against that team, or any team, for that matter.
"Tonight, for me, it was about the execution level, and for whatever reason, it wasn't very good."
Helm opened the scoring 7:09 into the game and added a spectacular shorthanded goal at 16:49 of the second. Alfredsson, playing in his 1,200th NHL game, sandwiched his goals around one by Gustav Nyquist in Detroit's three-goal third period.
Howard, who had been 0-3-4 in his previous seven starts, looked sharp in his return after coach Mike Babcock played Jonas Gustavsson in victories against the Buffalo Sabres on Sunday and the Boston Bruins on Wednesday. The shutout was Howard's second of the season and the 18th of his career.
"To be honest, I didn't really change much in my game," Howard told the Detroit Free Press. "I just fine-tuned a couple little things."
Detroit has outscored its opponents 14-2 in winning three in a row.
"It comes when we play good defense," captain Henrik Zetterberg told the Free Press. "Then we can make plays and play some good offense. But we have a good mix in our group; we've got four lines that can play both ways."
Kevin Poulin stopped 25 shots for the Islanders (8-15-3), who lost their fifth in a row since beating the Red Wings 5-4 in a shootout at the Coliseum 13 days ago. New York has dropped 10 of its past 12 games since opening November with victories against the Ottawa Senators and the Bruins, and is last in the Metropolitan Division with 19 points.
"We've got to play tomorrow [at home against the Washington Capitals], and we've got to find some answers," Islanders captain John Tavares said. "We're obviously an easy team to play against right now. We're not hard enough to play against, and you can tell why [Detroit has] had a lot of success for a lot of years now."
The Red Wings grabbed the lead on a quick defense-to-offense transition. Brendan Smith broke up a rush in his own zone and sent Alfredsson speeding away. Alfredsson carried the puck into the Islanders zone and dropped it for Helm, who deked past defenseman Radek Martinek, drew Poulin out of the net and slid home a backhander for his sixth goal of the season.
Howard, who stopped 12 shots in the first period, had to be sharp early in the second when Tavares set up Thomas Vanek in the slot. But Howard got to the right post and took Vanek's one-timer in the crest.
The Islanders got their only power play of the game when Justin Abdelkader was called for interference with 3:57 left in the second period. But it was the Red Wings who capitalized when Helm outraced Andrew MacDonald for a clearing attempt. Poulin came out of his net, but Helm got a piece of the puck before the two collided and it slid over the goal line for the first shorthanded goal allowed by the Islanders since March 29, 2012. It was Helm's seventh goal of the season; three have come against the Islanders.
"He's speedy out there," Howard told the Free Press. "Helmer's fun to watch, especially when he gets that energy going. He can be very impactful out there."
Alfredsson ended any speculation about the outcome when he took Smith's breakaway pass at the New York blue line, raced in alone and beat Poulin from between the hash marks 12 seconds into the third period for his fifth of the season. Six minutes later, Nyquist took a pass from Johan Franzen and beat Poulin to finish a 2-on-1 break. Alfredsson knocked in a loose puck with 3:47 remaining to complete the scoring.
The Islanders need answers now, with the Capitals coming to the Coliseum on Saturday and the Pittsburgh Penguins on Tuesday before they go on a trip out West.
"We're having a tough time coming out of our own end, and we're just not moving our feet and engaging," Tavares said. "We can't give them time and space like we did tonight. It's up to the guys in here. It's the same thing we've been saying for a while now. Game after game, there are big points slipping by, and we have to figure [things] out sooner rather than later."
Material from team media was used in this report