Barzal's breakaway goal made it 2-1. Josh Bailey forced Kakko into a turnover at the far blue line and sprung Barzal, who deked to his backhand and beat Shesterkin.
"Obviously in an important game like it was tonight, to give that goal up, it's tough on a young player," Rangers coach Gerard Gallant said, referring to Kakko. "But I saw [Chris] Kreider and Goodrow down there talking to him. You know, you're going to make mistakes, but it's nice that he finished it off the right way. It makes it a lot easier for him, for sure."
Gauthier helped ease Kakko's burden by scoring less than three minutes later to tie the game 2-2. He caught up to Goodrow's flip pass into the zone, skated through the right face-off circle and made a move to his backhand before sliding the puck through Sorokin's five-hole at 5:30.
"Honestly, I didn't even slow down a single bit," Gauthier said. "[The pass] was perfectly placed and pretty easy for me to get a scoring opportunity out of it."
But the Islanders got the lead back at 8:45 when Romanov scored his first goal of the season with a low shot from the left point through traffic to make it 3-2. It was their third goal on nine shots.
Goodrow tied it 3-3 at 3:00 of the third, scoring on a deflection of Gauthier's shot from above the left circle.
The Rangers limited the Islanders to five shots on goal in the third.
"We're up 3-2 on the road, it's a good spot to be," Barzal said. "Don't really know what to say. It obviously [stinks]."
NOTES: Islanders center Casey Cizikas left the game in the second period. Coach Lane Lambert did not provide an update. Cizikas has not missed a game this season. … Gauthier was a healthy scratch the previous three games. … Trocheck extended his point streak to six games (three goals, seven assists), tied for the longest in his NHL career. He has 13 points (four goals, nine assists) in the past nine games. … Islanders forward Jean-Gabriel Pageau played his 600th NHL game. … The Islanders lost for the first time when leading after the second period (11-1-0).