With Koskinen pulled for the extra skater, McDavid cut it to 5-4 at 18:10, but Copp scored into an empty net at 19:08 for the 6-4 final.
Draisaitl scored for the fourth game in a row to give the Oilers a 1-0 lead 1:48 of the first period, skating down the right wing before beating Hellebuyck five-hole on the power play. Copp tied it 1-1 with a power-play goal at 5:14.
"He hasn't changed his identity," Jets coach Paul Maurice said. "So he's not cheating the game to do it. He's true to his own game. He's a very, very strong defensive player that takes great pride in the penalty kill, so he's a little wounded tonight when they're scoring. But he's been honest about the way that he's generated his offense."
Adam Larsson scored for Edmonton to make it 2-1 at 9:13, and Ryan Nugent-Hopkins made it 3-1 on the power play at 11:16. The Oilers were 2-for-2 on the power play after going 1-for-18 in their previous five games.
Mathieu Perreault cut it to 3-2 at 14:37 of the first with a one-timer near the left hash marks three seconds after a power play expired.
NOTES:Maurice (737-649-122, 99 ties) coached his 1,607th NHL game, tying him with Al Arbour for fourth in NHL history. Scotty Bowman is first at 2,141 games coached. … Copp (four goals, five assists) and Lowry (four goals, three assists) each extended his point streak to an NHL career-high five games. … McDavid (two goals, five assists) and Nugent-Hopkins (two goals, three assists) each extended his point streak to four games. … Stastny has six points (two goals, four assists) in his past three games.