Reilly Smith scored for the third consecutive game and Marc-Andre Fleury made 37 saves for the Golden Knights (5-3-0).
"We stayed with it," Marchessault said. "I think we were the most dominating team out there, and we earned the right to get those two points."
WATCH: [All Senators vs. Golden Knights highlights]
Thomas Chabot and Jean-Gabriel Pageau scored, and Connor Brown had two assists for the Senators (1-5-0).
"It felt kind of like an old playoff game," Nilsson said. "Obviously we knew it was going to be a good atmosphere. Vegas has a good team and they came pretty hard at us, but I think we stood up pretty good and we were prepared for a battle."
Mark Stone had an assist, his 200th in the NHL, in his first game against the Senators since being traded to Vegas on Feb. 25 for defenseman Erik Brannstrom, forward Oscar Lindberg and a second-round pick in the 2020 NHL Draft.
"I'm happy for it to be done with," Stone said. "It'll be normal now, just a normal game. I don't know how everyone else takes it, but it is awkward a little bit, especially in a place where you enjoyed playing. A lot of close friends I'll always be friends with. It was tough in that sense, but once the game gets going, it's a hockey game. We're hockey players and we just play a normal game."