Martin Necas and Jordan Staal scored, and Frederik Andersen made 17 saves for Carolina (39-12-8), which has lost two straight.
"We let [Eichel] alone a couple of times. He's not going to miss," Hurricanes coach Rod Brind'Amour said. "We had a great third period. We did everything we had to do to get back in there. Unfortunately, we went to sleep for a second, then it's in the back of your net. We had a good start to the game. Little lull in the second, we didn't play our game that well. We made a couple of errors. We gave their best player a breakaway. All in all, I loved how we came back, we just had that one mental error in the third that cost us."
Eichel gave the Golden Knights a 1-0 lead at 5:11 of the second period, taking a pass from William Carrier and scoring high glove side from above the right circle.
"Shea [Theodore] makes a great play up to Will," Eichel said. "Will finds me and I'm just trying to use the [defenseman] as a screen, and good to see it go in."