Elsewhere, the Florida Panthers defeated the Winnipeg Jets by the same scoreline, extending their opponents' losing streak to eight games.
Hellebuyck inspires Devils against Vegas
New Jersey produced a strong performance on the road at T-Mobile Arena, with Hellebuyck stopping 19 of the 21 shots he faced to help the Devils secure their second victory with the three-time Vezina Trophy winner in goal.
The contest began at a lively pace, with both teams scoring twice in the opening period.
Luke Hughes opened the scoring for New Jersey before Mark Stone and Ivan Barbashev put Vegas ahead. Arseny Gritsyuk restored parity for the Devils, while Jack Hughes then gave the visitors a 3-2 advantage.
Gritsyuk scored again in the second period to extend New Jersey's lead. Jack Hughes added his second goal of the night into an empty net in the third period to complete the 5-2 victory.
Both Gritsyuk and Jack Hughes finished with two goals, while Luke Hughes also found the net.
The result improved New Jersey's record to 9-5-0, while Vegas dropped to 9-5-1.
Panthers condemn Jets to eighth consecutive defeat
The Florida Panthers also enjoyed a convincing night, beating Winnipeg 5-2 at Amerant Bank Arena to hand the Jets their eighth consecutive defeat.
Anton Lundell was the standout performer, scoring a hat-trick to help Florida secure its third successive victory.
Sam Reinhart opened the scoring in the first period before Lundell doubled the advantage early in the second.
Winnipeg responded through Kyle Connor, who scored on a five-on-three power play to reduce the deficit to 2-1.
Seth Jones restored Florida's two-goal cushion with a power-play goal, but Morgan Barron brought the Jets back within one in the third period.
Lundell then scored twice more, including an empty-net goal, to complete his hat-trick and seal the Panthers' 5-2 win.
Reinhart finished with a goal and an assist, while Jones contributed a goal and two assists. Goaltender Akira Schmid made 22 saves for Florida.
The defeat left Winnipeg with a 4-7-3 record and an eight-game winless run, comprising six regulation defeats and two overtime or shootout losses.
Hellebuyck's departure continues to shape Winnipeg's season
The results also highlighted the contrasting fortunes of Hellebuyck's former and new teams.
The goaltender joined New Jersey from Winnipeg on 23 October in a major trade. He had spent his first 11 NHL seasons with the Jets and won the Vezina Trophy three times during his career.
Winnipeg has since struggled to stop its losing run, while Hellebuyck has helped the Devils collect consecutive victories.
The Jets will need to address their defensive and goaltending problems as they look to regain momentum in the early stages of the campaign.
NHL results
• New Jersey Devils 5-2 Vegas Golden Knights: Arseny Gritsyuk (2), Jack Hughes (2) and Luke Hughes scored for New Jersey. Mark Stone and Ivan Barbashev replied for Vegas.
• Florida Panthers 5-2 Winnipeg Jets: Anton Lundell scored a hat-trick, while Sam Reinhart and Seth Jones also found the net for Florida. Kyle Connor and Morgan Barron scored for Winnipeg.