New York has a point in three straight games but is 0-8-3 since a 2-0 win at the Winnipeg Jets on Nov. 6 and has lost its first six games in its new home (0-4-2).
"The only thing I didn't like in the game is, really, the result," Islanders coach Barry Trotz said. "You look at the group, I thought we had a really good effort. … I look at the last three games, we've got a point in every game. We're playing hockey now. We're playing in a lot of areas the right way.
"The group understands. We would love to get our first win in the building here for our fans, for us, for our confidence. But we're just collecting points as we can. We'd like two, but we get one. It's better than nothing."
Patrick Kane scored the only goal in the shootout. Fleury made saves against Oliver Wahlstrom, Mathew Barzal and Anthony Beauvillier.
Fleury has saved all eight shots he's faced in three shootout victories this season and has won six of eight since a 1-7-0 start.
"[Fleury is] unbelievable. Vezina Trophy winner for a reason," Blackhawks forward Dylan Strome said. "Without him, we're not in a lot of these games. He's a heck of a goalie. ... One of the best teammates I've ever had for sure."
Strome gave the Blackhawks a 2-1 lead at 5:59 of the third. Erik Gustafsson attempted a pass to DeBrincat in the high slot, where Islanders defenseman Sebastian Aho backhanded it away but it went right to Strome, who scored on a wrist shot for his first goal in seven games.
Dobson tied it 2-2 with a slap shot blocker side after taking a pass from Barzal.
"I think I definitely had a few chances out there tonight," Dobson said. "It was nice to bury one in the last few seconds."
Brandon Hagel gave Chicago a 1-0 lead with a power-play goal at 6:49 of the first period. Hagel posted in front of the crease, where a one-timer from DeBrincat deflected off his leg and past Varlamov for his fifth goal in nine games.
"We're finding ways to win," Hagel said. "We're winning those 2-1, 3-2 games. That's what we have to do when the puck's not going in the net. Have to be happy with that. Hopefully, the pucks start going in, obviously."
