"I thought our start was really good and we put them on their heels a little bit early on, and that helps a lot," Draisaitl said. "We had contributions from all four lines, defensemen, and [goalie Mike Smith] was great, so it was a pretty complete effort."
Connor McDavid had a goal and two assists, Darnell Nurse had a goal and an assist, Tyson Barrie had three assists, and Smith made 21 saves for Edmonton (17-11-0) in the second of a three-game series which ends here Friday.
Edmonton, which has won 11 of 15, has won all six games against Ottawa this season.
"The whole game, we just didn't play the right way and we just didn't eliminate anybody," Senators coach D.J. Smith said. "We didn't stop anyone in the [defensive] zone, and we were easy to play against. We didn't look like we had a lot of jam, and they did. They had good legs, they jumped on every puck and they were ready to play, and we weren't."
Evgenii Dadonov scored, and Matt Murray made 29 saves for Ottawa (9-19-1).
"They're a power team, they have so much skill up front and they're hard to play against and hard to defend," Senators defenseman Thomas Chabot said. "You know these guys are going to score, they're going to have chances, they're going to have looks, and that's what we have to do. We have to limit those, we have to play them harder."
Nurse scored at 3:52 of the first period on a shot from the point through traffic to give Edmonton a 1-0 lead. The Oilers controlled the puck in the Senators zone for nearly a minute prior to the goal.
Jujhar Khaira made it 2-0 at 5:57 on a pass from Devin Shore on a 2-on-0 following a turnover by Dadonov.
Draisaitl scored on an individual rush at 12:08 for a 3-0 lead, and McDavid made it 4-0 at 13:26 on a shot from the slot.
"[Draisaitl] is such a strong player," Oilers coach Dave Tippett said. "He holds the puck, he uses his body well, forehand, backhand, it doesn't seem to matter to him. He's got so much poise in tight spots. He's an elite player. When you put the two of them together [with McDavid], it's a pretty lethal combination."