Neal gave the Oilers a 1-0 lead at 9:11 with his 11th goal, eighth on the power play. Draisaitl got his 200th NHL assist on the goal.
"He's very confident right now, and he's fun to have on the ice," Edmonton defenseman Oscar Klefbom said of Neal. "He's going to be a very important piece for us because the power play's so important for teams who are going to make the playoffs."
Draisaitl made it 2-0 at 17:02, three seconds after the Oilers' third power play of the period expired. Alex Chiasson's shot from the left point rebounded to Nugent-Hopkins, who passed to Draisaitl low in the right face-off circle for a one-timer.
"When you're playing a team on a back-to-back, you want to get on them right away," Blue Jackets coach John Tortorella said. "To let their top players touch the puck as much as they did in the first period to get themselves into the game, you're pushing an uphill battle.
"We didn't climb the hill after that. We didn't climb it."