Filip Hronek, Sam Gagner and Givani Smith also scored for the Red Wings, who won their season-high fifth straight. Alex Nedeljkovic had 20 saves.
"This wasn't our best game, but we have that swagger and confidence now," Seider said. "We have an ability to stick together and win these games somehow."
Oliver Wahlstrom had two power-play goals, Cal Clutterbuck scored short-handed, and Mathew Barzal had two assists as the Islanders earned a point for the second straight game and fell to 0-8-2 during their skid. Ilya Sorokin finished with 26 saves.
"We had the power play working, but we can't expect to get all of our goals that way," Wahlstrom said. "We have to find a way to get some goals at 5-on-5 if we want to win games."
In the extra period, Seider scored on a one-timer from the left circle off a pass from Pius Suter.
"(Seider) has got a good swagger and a good way of rising in the moment," Red Wings coach Jeff Blashill said. "And, he certainly rose in that moment."
The Islanders, missing leading scorer Brock Nelson and defenseman Ryan Pulock due to injuries, matched the longest winless streak in franchise history, a similar 0-8-2 stretch from Nov. 19 to Dec. 9, 2013. They managed just 23 shots on goal — only three in the first period — and scored more than one goal for just the second time in nine games.
Wahlstrom's second of the night tied it 3-3 with 7 1/2 minutes left in the third period.
"We need to find a way to finish one of these games," Barzal said. "We can't give away points."`
The Islanders opened the scoring when Clutterbuck wrapped around Filip Zadina and tucked the puck past a sprawling Nedeljkovic 2:45 into the game.
Hronek tied it from beyond the left circle at 5:18 of the first, and Gagne banked a shot off Sorokin's right shoulder pad on a sharp angle at 7:37 to put the Red Wings ahead.
"Guys have stepped up in big moments," Blashill said. "These games are so close throughout the league, it's about who steps up in a big moment, and we've had some guys do that."
Wahlstrom snapped a nine-game pointless streak to tie it 2-2 midway through the second period.
Smith gave the Red Wings a 3-2 lead on a shot that whistled over Sorokin's left shoulder for his fourth point in seven games. The 6-foot-2, 215-pound forward, who was protected by the Red Wings in July's expansion draft, was held without a point the first 12 games of the season.
"He's been up and down, in terms of his play, but I thought this was maybe the best, complete game he's played," Blashill said. " We just didn't get him out there as much as he deserved, but if he keeps playing like that, you'll start getting more minutes".
Red Wings D Gustav Lindstrom exited in the second period with a lower-body injury. ... Red Wings F Joe Veleno rejoined the team after missing the past three games with an upper-body injury. ... Red Wings D Danny DeKeyer, who missed the previous four games (COVID-19 protocol), was a healthy scratch. ... Islanders D Zdeno Chara cleared COVID-19 protocols and returned after a three-game absence. ... Islanders D Robin Salo was a healthy scratch for a second consecutive game. … Casey Cizikas is the lone Isles player remaining in COVID-19 protocol after two scheduled games were postponed earlier this week due to a COVID-19 outbreak.
Red Wings: Host Nashville on Tuesday to conclude their three-game homestand.
Islanders: Host Chicago in the second of a back-to-back Sunday.
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