Steve Payne and Neal Broten each had three goals for Minnesota during the tie in Uniondale, N.Y.
Vaunted Islanders goalie Billy Smith was routed for the second straight game, replaced by Roland Melanson during the second period.
The lead seesawed until Tim Young gained the North Stars the final deadlock with 5:28 remaining.
The Islanders got the first two goals, 34 seconds apart in the opening period. Mike Bossy beat goalie Gilles Meloche with a backhander off a nice feed by Bryan Trottier at 4:49, then Bossy returned the favor by springing Trottier for a breakaway at 5:03.
After Payne scored his first of the night by tipping Dan Mandich's weak backhander past Smith, New York's Wayne Merrick got his first of the season on a rebound.
The North Stars came back with a goal by Broten on a beautiful move around defenseman Gord Lane and a short shot that hit Stefan Persson's stick and hopped over Smith. Payne made it 3-3, putting the puck into an unguarded cage after goalie Smith foiled Bobby Smith's wraparound shot.
Minnesota continued its rally in the middle period. Broten connected at 1:51, firing over Smith. At 5:33, Bobby Smith drove the goalie to the bench; the North Stars' center put his own rebound past Smith.
Then it was New York's turn to rally. John Tonelli tipped home Bossy's slap shot at 10:06 and, 2 1/2 minutes later, Anders Kallur tied it with a wrist shot from the slot.
Payne completed his fifth career hat trick 42 seconds into the final period, backhanding a rebound; Lane tied it again with a slap from the point, only to have Broten make it 7-6 with a short-handed effort.
Denis Potvin slapped home a long power-play shot; Trottier a rebound of his own shot, and Young a power-play slap shot which deflected off the stick of New York's Butch Goring and soared past Melanson.