Ryan Shea threw the puck along the left boards, where it bounced off Connor McDavid’s knee and slid through the slot to Draisaitl, who chipped the puck past a lunging Philipp Grubauer from in front.
McDavid had a goal and an assist, and Owen Michaels also scored for the Oilers (2-0-1). Devon Levi made 19 saves.
Bobby McMann scored for the Kraken (1-1-0), who face the Calgary Flames at Climate Pledge Arena on Sunday for the second of a back-to-back set. Grubauer made 22 saves.
Edmonton went ahead 1-0 at 2:51 of the first period when Michaels took a short pass along the boards from Alex Formenton, skated in past the left face-off dot and sent a wrist shot near side into the top corner.
It was Michaels' second goal in as many games after scoring the first of his NHL career in a 9-7 win at the Vancouver Canucks on Thursday.
McMann tied it 1-1 on the power play at 9:06 of the second period, taking a Jordan Eberle pass from below the goal line and lifting the puck past Levi’s blocker from the left circle.
At 7:38 of the third period, Levi appeared to stop a point-blank shot by Eberle, which went to review before being confirmed that the puck did not cross the goal line.
McDavid scored into an empty net to secure the 3-1 final at 18:55.