Koskinen's win total is tied for the NHL's best this season. Ryan Nugent-Hopkins, Zach Hyman and Jesse Puljujarvi scored for the Oilers.
Chandler Stephenson and Reilly Smith scored for Vegas, while Robin Lehner made 27 saves.
Edmonton pushed its lead to three goals when Evan Bouchard sent a rink-length pass into the offensive zone, where Puljujarvi entered on a breakaway and beat Lehner to snap an eight-game goal drought with his seventh of the season.
Stephenson responded with his third goal in three games, whipping past two defenders and finding a leak between Koskinen and the post. Vegas got within a goal when a loose puck in front of Koskinen was batted in by what replays appeared to show Jonathan Marchessault connecting with a backhand, but was credited to Smith for his ninth goal of the season _ tied for the team lead.
But Vegas couldn't score again.
The game started with brilliant performances by both goaltenders over the first 17 1/2 minutes, but a pair of Golden Knights turnovers did Lehner no favors in a span of 1:54 late in the period.
First, it was Nugent-Hopkins keeping the puck on a 2-on-1 rush and going far side to beat Lehner for his second goal of the season and 498th career point.
Then, with 16 seconds left in the first, Hyman fought off Vegas' Mark Stone as they entered the zone, and beat Lehner with a backhand to give Edmonton a two-goal lead and registering his ninth goal of the season and 200th career point.
It marked the eighth straight game the Golden Knights were either up or down at least 2-0.
Edmonton: Hosts Pittsburgh on Wednesday.
Vegas: Visits Anaheim on Wednesday.