Alex Chiasson then gave the Oilers a 3-2 lead at 16:37, gathering the rebound of Draisaitl's shot and tucking the puck inside the right post on the power play.
"Every time you don't win the last game of the year then it's disappointing," Edmonton coach Dave Tippett said. "But I thought our team took some strides this year. We were expecting more in the playoffs. It was a tight, tight series. We couldn't find a way to get on top of it.
"I give our players credit, they battled hard. That's not an easy game. We didn't get the result we wanted last night. You come in here and you've got to play a back-to-back, and a lot of players played real well. It's just disappointing we couldn't get the win."
Scheifele's second goal of the game tied it 3-3 at 6:01 of the third period. He scored with a slap shot from the left circle following a turnover by Oilers defenseman Ethan Bear.
"We had faith in our room," Scheifele said. "We trusted the process, and by doing the right things over and over and over, we knew that we were going to come out on top. Whenever that adversity hit -- they scored a goal, or we took a penalty, kill off a 5-on-3 -- whatever that was, we stuck with it. I think it just speaks volumes for this room, the character we have in this room. Guys just never get down. We don't get down on ourselves. We stuck with our game plan, and because of that, we came out on top."
NOTES:It was the first time the Jets swept a playoff series in their history. … Oilers defenseman Darnell Nurse played 62:07, including 15:32 in the first overtime. It is the most by an Edmonton player since 1997-98, when time on ice was first officially tracked.