Marchessault beat Senators goalie Craig Anderson blocker side on a penalty shot.
"Obviously, I was excited," Marchessault said. "But as a group, we needed that game before going on a two-game road trip]."
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Anderson said, "[Marchessault is] a good shooter there, probably one of their best skilled guys. Made the perfect shot, just inside the post, over the pad."
Ryan Dzingel had a goal and an assist, Thomas Chabot had two assists and Anderson made 49 saves for Ottawa (4-4-2), which has lost three straight.
"[Anderson] was our best player tonight," Senators forward Matt Duchene said. "He was outstanding and a huge reason why we got the point."
Alex Tuch scored twice, Erik Haula had two assists and Marc-Andre Fleury made 19 saves for Vegas (5-5-1), which set a team record for shots in a game with 53. Its previous high was 49 against the St. Louis Blues on Oct. 21, 2017.
"We had a ton of shots and a ton of chances early on in the game and nothing was going in," Golden Knights coach Gerard Gallant said. "We just stuck with it, kept working hard, and I thought we played an excellent game."