"He's doing the right things, he's leading by example, he's making the right decisions with the puck," Sabres coach Phil Housley said. "I know the first game he tried to do too much. He's trusting his teammates now, so it's good to see him playing well."
Jason Pominville and Marco Scandella scored, and Carter Hutton made 35 saves for Buffalo, which has won two in a row after losing its season opener and has a winning record for the first time since Jan. 24, 2013.
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"It's a credit to our guys," Housley said. "Obviously, there's a lot of things that we still need to clean up. But it's a credit to them. They've put the work in and now they're getting results, which is great for their confidence."
Erik Haula and Jonathan Marchessault scored, and Marc-Andre Fleury made 13 saves for Vegas.
"We didn't play good enough to win the hockey game," coach Gerard Gallant said. "I'd like to say just because we had a lot of shots ... they were the better team. They were more committed to winning today and we didn't show up good enough."
Eichel gave the Sabres a 1-0 lead at 14:31 of the first period with a one-timer from the left face-off circle on the power play. He extended the lead to 2-0 after he received a pass from Sam Reinhart in the slot, deked Fleury, and scored on the backhand at 4:58 of the second period. It was the Sabres' first goal at 5-on-5 this season.