Vegas outshot the Islanders 47-21 on Thursday, including 31-16 in the second and third periods.
The Golden Knights comeback started with Brandon Pirri's power-play goal at 8:48 of the second period and essentially ended when William Karlsson and Paul Stastny scored 1:03 apart in the third period.
Vegas applied constant pressure from Pirri's goal to Nate Schmidt's empty-netter and the Islanders couldn't seem to swing the momentum, not even after an offside challenged overturned a Knights goal in the second period.
"They played well, they were the better team tonight," Josh Bailey said. "We were still in a position to win the game tonight and I think that's where a little bit of frustration comes in. We let it slip away. We'll talk tomorrow about it, learn from it and be better for it."
Thomas Greiss made 43 saves in the loss, while Marc-Andre Fleury made 19 in the win. Fleury clamped down after giving up the two quick strikes to Barzal and Nelson, robbing Barzal in the final minute of the second period.
There was a bit of frustration from the Islanders bench after Oscar Lindberg's high hit on Johnny Boychuk at 5:21 of the third period. Anthony Beauvillier stepped up to defend Boychuk and wound up with an offsetting roughing minor instead of a power play, with Karlsson scoring on the ensuing four-on-four.