The loss was Winnipeg’s sixth straight at home and ninth in their last 10 home games.
Centre Mark Scheifele had given the Jets a 3-2 lead with 2:03 remaining in regulation on his second goal of the game.
But the Islanders took advantage of an extra attacker and Nick Leddy sent the match into overtime when he got a good screen in front of Hutchinson and tied it with 29 seconds left.
Hutchinson turned aside 23 of the 27 shots he faced for the Jets (26-32-5), while Tyler Myers also scored.
Prince put the Islanders ahead 2-1 at 8:32 of the third period, but Jets defenceman Myers quickly evened it up at 9:56.
It was the sixth game in a season-high seven-game road trip for the Islanders (5-1-0), including a shootout win over Calgary.
New York went into the game with the NHL's top penalty kill, but the Jets scored on the power play at 16:13 of the first period while Johnny Boychuk was in the box for roughing.
It was Scheifele's 16th goal of the season, a career-high for the third-year centre that he bumped up to 17 with his second marker of the night.
The assist extended Byfuglien's point streak to seven games, with one goal and six assists. Perreault also marked a career-high 26th assist of the season.
Jets forward Anthony Peluso left the game in the first period after crashing into the net and didn't return because of what the team called an upper-body injury.
De Haan tied it at 6:02 of the second after Manitoba native Travis Hamonic passed the puck out of the corner to de Haan in front and his point shot beat Hutchinson.
Winnipeg had a 20-16 edge in shots on goal after the second.
Prince scored his fourth goal of the season after withstanding a slash around his right hand by Byfuglien as he went the net.
Myers' tying goal was his seventh of the season.
The Islanders wrap up their road journey Sunday against the New York Rangers.
Winnipeg hosts the Montreal Canadiens on Saturday.