Lavoie scored at 8:01 of the third period after finishing the rebound on the rush following a Ville Heinola shot to give Vegas a 2-1 lead.
The forward was originally expected to be a healthy scratch, but goalie Carter Hart sustained an undisclosed injury at the morning skate.
Braeden Bowman, William Karlsson and Jack Eichel scored for the Golden Knights (9-4-1), who lost three in a row (0-2-1). Adin Hill made 24 saves starting in place of Hart.
Shane Pinto scored for the Senators (8-5-0), who were coming off a 7-4 victory against the New York Rangers on Saturday. Jonas Johansson made 25 saves.
Bowman put the Golden Knights ahead 1-0 at 19:49 of the second period on the power play. He scored after Ivan Barbashev’s shot fell short of the goal line where Bowman was parked. The play started when Hill darted out to the face-off dot to beat Ottawa’s Ridly Greig to the puck, breaking his goalie stick in the ensuing collision.
Pinto tied the game 34 seconds into the third period on the power play. Drake Batherson recovered an errant pass near the blue line, skated up the boards and found Pinto coming down the middle of the ice to beat Hill on the rush to make it 1-1.
Karlsson scored the empty-net goal at 18:00 to make it 3-1; Eichel scored another empty-net 19:53 for the 4-1 final.
The Golden Knights recalled goalie Cameron Whitehead from Henderson of the American Hockey League to back up Hill, and forward Jonas Rondbjerg was assigned to Henderson.
