Brisson was selected 29th overall in the 2020 NHL Entry Draft.
Jack Eichel scored twice, and Logan Thompson secured his 10th win.
Vegas went a combined 0-for-17 in three straight shootouts to end the year.
Vegas must win and Dallas must lose to keep the dream alive.
The Golden Knights must win out and need Dallas to lose twice in regulation.
An overview of where things stand heading into the final week of the regular season.
San Jose tied the game to force overtime with 0.9 seconds left in regulation.
The Golden Knights could be without their No. 1 goalie for the homestretch of the regular season.
Vegas turned the game around with two goals in 49 seconds early in the third period.