Parenteau banged home a cross-ice pass from John Tavares as the Islanders found themselves on a power play during the extra period when a frustrated Henrik Zetterberg was called for a holding penalty after missing a wide open net.
Tavares ended the game with a goal and two assists for the red-hot Islanders, who have knocked off Pittsburgh and Detroit, the NHL's top two teams, in back-to-back games and have taken six of eight overall.
Tomas Tatar scored the game-tying goal in his NHL debut as the Red Wings had their three-game win streak snapped. Johan Franzen and Valtteri Filppula also scored in the loss, while Jimmy Howard surrendered four goals on 23 shots.
The Red Wings tied the game at three on Tatar's first career goal with 9:42 left to play. He was able to get a piece of Darren Helm's shot from the point and the puck trickled past Roloson's left leg.
The game remained deadlocked the rest of the way to force the extra period.
Detroit got on the board first after Zetterberg circled behind the net and sent a pass to a streaking Franzen, who chipped it in from the lower right circle with just over eight minutes left in the opening period.
The Isles tied it up just five seconds after Todd Bertuzzi's interference penalty at the 13:17 mark. Tavares' offensive zone face off win went to Andrew MacDonald, who sent a shot toward the net. Howard blocked the initial shot, but Moulson was able to swipe the rebound into the net.
New York took a 2-1 lead with three seconds left in the first, off another offensive face off win, when Tavares ripped a shot past the Detroit netminder.
At the 15:13 mark of the second period, the Islanders got another tally off a face off win where Milan Jurcina fired a slap shot from the point and Joensuu was able to tip the puck past Howard.
Detroit cut the deficit in half with nine seconds left in the middle session when Darren Helm shot the puck and it was deflected in the air off a sprawling Roloson. Filppula plucked the puck out of the air, placed it on the ice and chipped it into the open net.
New York has won three straight and four of the last five meetings. Franzen's goal was the Red Wings' first goal against the Islanders since 2007...Detroit was 0-for-5 on the power play, while the Islanders were 2-for-2...Helm had two assists in the loss, while MacDonald added two helpers for New York.