Fasching cut it to 3-2 at 14:31, kicking a pass from Casey Cizikas onto his stick for a wrist shot just outside the crease.
Lee tied it 3-3 with his second of the game at 18:45 by redirecting a shot from Noah Dobson.
"We stick with our game," said Lee, the Islanders captain. "We play the way we have been, we did it the last 20 [minutes], on our forecheck, our guys can make plays and score goals. Down 3-1, it's definitely a big task. It's not going to happen every night, but we believe in ourselves."
New York had 13 shots on goal in the third period after being held to 13 in the first two.
"They played a full 65 [minutes]," Jarry said. "We were able to push the first and second period. I think just a little bit of puck mismanagement in the third period. A couple of bounces went their way."