Halliday left the game in the third period and did not return after being checked into the side glass of the Vegas bench.
Fabian Zetterlund scored, and Brady Tkachuk had three assists for the Senators (24-21-7), who had lost four of five (1-2-2), including a 4-1 defeat to the Carolina Hurricanes on Saturday. Mads Sogaard made 19 saves for his first win of the season.
Sogaard, who was recalled from Belleville of the American Hockey League on Saturday, was making his second appearance for Ottawa this season.
Rasmus Andersson scored his first goal with the Golden Knights (25-14-12), who have lost three of their past four games. Adin Hill made 24 saves.
Mark Stone’s 14-game point streak ended for Vegas (12 goals, 11 assists).
At 1:36 of the first period, Vegas forward Mitch Marner was awarded a penalty shot after being hooked on a breakaway, but he was unable to get a clear shot off against Sogaard.
Ridly Greig appeared to score the game’s first goal at 5:43 for the Senators after jamming the puck across the goal line, but it was quickly waved off for goaltender interference against Greig.
Fabian Zetterlund gave Ottawa a 1-0 lead at 9:25, banking the puck in off Vegas defenseman Kaeden Korczak’s skate from behind.
Cozens extended it to 2-0 at 5:51 of the second period after receiving a feed from Greig in the crease and tapping it in on one knee on the backhand.
Jordan Spence scored 16 seconds later to push it to 3-0 at 6:07 when his shot through traffic found its way past Hill.
Halliday scored the Senators' third goal of the period to make it 4-0 at 17:50 with a wrist shot from the right circle glove side.
Cozens’ second goal of the game extended it to 5-0 at 1:22 after he took a pass from Tkachuk in the slot and finished top right corner.
Halliday scored his second goal to make it 6-0 at 2:05 of the third period on a shot from the point.
Nick Jensen pushed it to 7-0 at 3:56 of the third period after banking the puck off Vegas defenseman Noah Hanifin’s stick.
Andersson, who was traded to Vegas by the Calgary Flames on Jan. 18, made it 7-1 at 15:05 of the third to make it 7-1.
