Cuylle gave the Rangers a 1-0 lead in the last second of a power play at 16:39 of the first period. He scored off a rebound of Jacob Trouba's shot from the right point.
Reinhart made it 1-1 at 10:11 of the second period with his League-leading 25th power-play goal off a highlight-reel setup by Barkov.
Carter Verhaeghe played the puck up to Barkov, who tipped it up and juggled it in the air, playing it to himself to get around K'Andre Miller. Falling forward, Barkov, with his stick stretched in front of him, moved the puck left to right past Vincent Trocheck, who tried to block the pass with his skate, to Reinhart for a tap-in from the right post.
"It just happened quick," Barkov said. "The puck was in the air. I just tried to make it flat on my stick. 'Rhino' was there backdoor, and I got the puck to him."
Reinhart said he wasn't surprised to see Barkov make that kind of play.
"I had a pretty good vantage point watching him make that play," he said. "Pretty nice and kind of expected out of him."
Lomberg said Barkov, "Doesn't even understand how sick it was."
He said he was still shocked at the play after the game.
"He's so nonchalant that that, to him, was just like another assist because that's how he carries himself, but being able to watch that live and see the team's reaction, it was a pretty sweet goal," Lomberg said. "I mean, how many times do you see a guy touch it out of the air over a defender and then one touch, two touch, backdoor tap in. Pretty special play."
Barkov and Reinhart connected again to make it 2-1 at 12:56 with Reinhart scoring on a one-timer from between the circles off a give-and-go with Barkov from the right boards.
Reinhart has 44 goals, including five in the past three games.
Kreider tied it 2-2 with a power-play goal at 15:26 off a rebound of Trocheck's shot.
Lomberg made it 3-2 at 6:11 of the third period with a 51-foot wrist shot from the top of the left circle past Shesterkin on the glove side. The puck appeared to graze off of Trouba's skate as it was released.
"I pick the puck up and had a little bit of space to skate it in," Lomberg said. "Threw it in between Trouba's legs there, and obviously, it found the back of the net."