Ryan McLeod and Jason Zucker also scored, and Byram had two assists for Buffalo (26-33-6), which has won two of three after a six-game skid (0-5-1). Ukko-Pekka Luukkonen made 16 saves.
Brett Howden and Pavel Dorofeyev scored, and Adin Hill made 34 saves for Vegas (39-19-8), which has lost three of four (1-1-2) and visits the Detroit Red Wings on Sunday.
“I just think a total lack of respect, probably most of the night,” Golden Knights coach Bruce Cassidy said. “But the way it kind of ended probably sums that up.”
Vegas forward Tomas Hertl had a chance to seal the game with an empty-net goal with under 40 seconds remaining in the third but opted to pass to Eichel, which led to a turnover.
“I’d like to see him shoot the puck in the net and end the game,” Cassidy said. “That’s what I’d like to see. I think the whole team would like to see that.”
Howden gave Vegas a 1-0 lead at 12:07 of the first period, taking a feed from Tanner Pearson at the back door and directing it past Luukkonen.
Dorofeyev put on a backhand from the side of the net behind Luukkonen, who was at the top of his crease, to make it 2-0 at 12:06 of the second period.
McLeod cut it to 2-1 seven seconds later at 12:13 when he took a stretch pass from Jacob Bryson at the offensive blue line and carried it to the left circle before beating Hill five-hole.