Mark Scheifele scored his 35th goal of the season,
Axel Jonsson-Fjallby
had a goal and assist, and Saku Maenalanen had two assists for the Jets (35-25-2), who have lost their past five games (0-4-1) and remained five points ahead of the idle Calgary Flames for the second wild card into the Stanley Cup Playoffs from the Western Conference.
Winnipeg hosts Edmonton on Saturday.
"I've never coached a team, I don't think, that was so undisciplined and took so many penalties," Jets coach Rick Bowness said. "You play a third of the game short-handed against that team, they're going to make you look bad and they made us look bad tonight."
Connor Hellebuyck allowed four goals on 24 shots before being replaced at the start of the third period by David Rittich, who made seven saves.
Draisaitl gave the Oilers a 1-0 lead at 2:06 of the first period, scoring on a one-timer from the goal line on a power play, and Nugent-Hopkins made it 2-0 at 1:44 of the second period when he intercepted a clearing attempt by Dylan DeMelo and scored from the slot.
Yamamoto extended it to 3-0 at 9:18 after receiving a stretch pass from Nugent-Hopkins, and made it 4-0 just 40 seconds later when a centering pass by Klim Kostin bounced off the skate of DeMelo before he stepped into the shot in the right face-off circle at 9:58.
"Anytime you're playing with 'Leo' and 'Nuge' it's pretty easy to get going as well," Yamamoto said. "I'm happy I got two on the board and an assist, but it was a good team win."