Voronkov made it 1-1 on the power play at 9:45 for his first goal in 13 games since March 7.
Horvat put the Islanders ahead 2-1 at 13:48, scoring for a third straight game.
Marchenko tied it 2-2 at 17:22 from behind the net, extending his goal streak to three games. He flipped the puck off the mask of Sorokin at the left post for his 21st goal, matching his total from last season as a rookie.
“It happened so quick,” Marchenko said. “I remember [Sidney] Crosby goals like, six maybe, years ago. He scored two goals just shooting [at] the head. It's in my head. I think about that. If I have opportunity, I try to do it.”
Tarasov left the game after Blue Jackets defenseman David Jiricek inadvertently clipped him in the side of the head with his hip while the goalie was covering the puck at the left post. Vincent had no update on him.
“It's hard to see Daniil going down like this,” Vincent said. “He's been playing so good, created some momentum for himself and for the team and just unfortunate.”
Greaves, in his fifth NHL game, stopped all 14 shots he faced in the second period.
“It's about winning hockey games at the end of the day,” he said. “So, there's obviously things to improve and some positives to take from it, as well.”
Islanders coach Patrick Roy liked the way his players stayed composed.
“Our mindset was really good,” he said. “We didn’t get frustrated because it was a 2-2 game. … Team effort was really good. It was a big goal by Noah so I was happy to see him scoring that goal, but more than that the way he was playing defensively. He had a strong game defensively.”
NOTES: Barzal has nine points (three goals, six assists) in his past eight games. … Horvat has scored in three straight games for the third time this season (March 5-10, Dec. 15-19). … Voronkov’s 18 goals are the third-most in a season by a Blue Jackets rookie, trailing Marchenko and Pierre-Luc Dubois (20 in 2017-18).