Mattias Janmark had a goal and an assist, Klim Kostin scored for the third straight game, and Zach Hyman had two assists to help the Oilers win their third straight to finish a 3-1 road trip. Jack Campbell had 27 saves.
Draisaitl had his 50th career two-goal game, and has four goals in the last three games.
He and teammate Connor McDavid have been especially good against the Knights. Draisaitl has 20 points in 17 career games against Vegas, and McDavid has 20 points in 16 games. McDavid's first-period assist extended his points streak to seven games (five goals, six assists).
The Oilers opened the game with Janmark and Draisaitl scoring on two of the first four shots on goal, taking a 2-0 lead just 1:42 into the game. Edmonton dominated the Knights in the first period, outshooting them 16-8, but the Oilers didn't add to the lead.
Vegas struck with 1:14 remaining in the period when Kolesar shot from behind the goal and the puck went off Campbell and into the net to make it 2-1. Kolesar has six points in six games (two goals, four assists).
The Oilers twice went ahead by two goals in the second period — from Draisaitl and Kostin — but the Knights answered time. Cotter and Karlsson's goals kept Vegas right there, trailing 4-3 entering the final period.
This was Vegas' first game without captain Mark Stone, who suffered an upper-back injury Thursday against Florida and is listed as week to week by Knights coach Bruce Cassidy. Stone underwent back surgery in May, but said recently he felt especially healthy. He is second on the Knights with 17 goals and 38 points.
Oilers: Host Seattle on Tuesday night.
Golden Knights: Host Dallas and former coach Pete DeBoer on Monday night.
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Mark Anderson, The Associated Press