Cizikas scored again on a one-timer off a pass from Thomas Hickey to give the Islanders a 4-0 lead at 15:25.
Farabee made it 4-1 on an odd-man rush at 17:52 of the first with a wrist shot from the right circle.
Sorokin made 11 saves in the second period to preserve New York's three-goal lead, then gloved Claude Giroux's point-blank chance at 7:05 of the third. The rookie goalie has allowed 10 goals during his seven-game winning streak.
"The team, of course, helps a lot," Sorokin said. "Every time I'm on the ice, I feel the team is always on the attack, and that always helps my game."
Anthony Beauvillier scored his first goal in nine games to make it 5-1 at 9:45 of the third period, and Josh Bailey scored at 15:46 for the 6-1 final.
Hickey had two assists in his first NHL game since May 3, 2019, which was Game 4 of the Eastern Conference Second Round against the Carolina Hurricanes.
"As soon as I got to the rink, I just flipped a switch," Hickey said. "I think that's a testament to the work I put in. I felt ready right away. … It's the best feeling I've had in a long time."
NOTES: Vigneault said he is unsure if Couturier will be able to play Monday. Couturier participated in warmups, but he and the training staff determined he should not play. … Flyers forward Michael Raffl was minus-1 with two hits in 14:18 after entering the lineup with Couturier a late scratch. … Wahlstrom had two assists and has a three-game point streak (two goals, two assists). … Islanders defenseman Noah Dobson remained on the NHL COVID-19 protocol list and missed a fourth straight game.