Roy extended the lead to 3-1 at 9:07 of the second on a rebound in front. The goal came after Noah Dobson gave the puck away to Barbashev in the neutral zone.
"Turnovers are going to happen," Islanders captain Anders Lee said. "And it's a fast game. Things happen at high speeds, and guys are trying to make plays. So, it's going to happen at times. But in terms of an overall game, I think we limited that really well and played a pretty solid hockey game."
Pageau scored a short-handed goal to cut it to 3-2 at 9:26 of the third period, beating Hill glove side from the top of the left circle.
"It was a big game for us to take care of," Golden Knights forward Jonathan Marchessault said. "We were not proud necessarily of our record on the road (10-9-4), and it's just good to get a win tonight."
NOTES: Barbashev extended his point streak to four games (three goals, four assists), and Marchessault had an assist to extend his to five (five goals, three assists). ... Nelson's goal was his 500th NHL point. ... Islanders forward Bo Horvat took a puck to the face with 31 seconds left in regulation. There was no update postgame.