Thomas Greiss allowed three goals on 11 shots in 11:56. Semyon Varlamov, who signed a four-year contract with the Islanders on July 1, made 17 saves in relief.
"We've had a tough stretch and it's within this room that we have to check ourselves a little bit here and reset, because we're not playing the way we had been that got us to this point and these last five games haven't been our identity," Islanders forward Anders Lee said. "We haven't played to who we are. We have to figure this out quickly."
Johnston finished a give-and-go with Josh Bailey to give the Islanders a 1-0 lead at 5:50 of the first period.
Gilbert, playing his 16th NHL game, slipped a backhand from the slot between Greiss' legs to tie it 1-1 at 7:34.
"I always joke around that I always go five-hole in practice, I always go five-hole in pregame warmups on my last shot before I go off the ice," Gilbert said. "It was kind of funny that it ended up being a five-hole goal of all things to squeak through."
Dominik Kubalik gave the Blackhawks a 2-1 lead at 9:46 when his one-timer from the slot re-directed off the stick of Islanders forward Nick Leddy. It was his third goal in the past four games.
"I'm just trying to work around the net, and I try to be open in the slot," Kubalik said. "That's what I'm trying to do and it's working right now."
Alex DeBrincat ended an eight-game goal drought, scoring on a wrist shot from the high slot at 11:56 to increase the lead to 3-1.
Jonathan Toews made it 4-1 from the right face-off circle 50 seconds into the third period.
Matthew Highmore scored his first of the season when his cross-ice pass banked off Islanders defenseman Ryan Pulock to make it 5-1 at 3:03.
Cizikas scored shorthanded at 16:32 for the 5-2 final.
"You get as much as you put in, and we haven't put enough in lately in terms of our structure, commitment, even our accountability to each other," Islanders coach Barry Trotz said. "We got a little cheat in our game, I think we're playing full. It's hard to be hungry when you're full."
