Tkachuk scored at 16:06 to make it 5-2, and Drake Batherson cut it to 5-3 on the power play at 17:38 with his first goal.
McDavid scored on the power play 42 seconds into the second period to put the Oilers ahead 6-3. Darnell Nurse made it 7-3 at 11:31.
Edmonton was 4-for-5 on the power play.
"Certainly, we have to flush it, you can't let it linger, but we're going to have to look at it and see what happened," Senators coach D.J. Smith said. "Four power-play goals, it's pretty easy to see what happened tonight. And you're playing catch-up all night against a team that has as much power as they do, it's one of those ones, it's probably best to flush."
Kailer Yamamoto made it 8-3 at 19:43 off a pass from Draisaitl, who leads the NHL with 15 assists and is second to McDavid with 21 points.
Tim Stutzle
scored on the power play at 8:08 of the third to make it 8-4, and Austin Watson scored 47 seconds later to make it 8-5 at 8:55.
It was the first NHL game between Stutzle and Draisaitl, who were born in Germany.
"You can't really say it was fun because, I think, he had six points tonight," said Stutzle, the No. 3 pick in the 2020 NHL Draft. "It's not a lot of fun playing against him. It's always tough playing against those very good players, and you could see what he did out there. We had some good shifts against him, and we have another game in two days, and that's our goal, to win that game."
NOTES: Gretzky had seven assists for the Oilers on Feb. 15, 1980 (8-2 win against Washington Capitals), Dec. 11, 1985 (12-9 win at Chicago Black Hawks) and Feb. 14, 1986 (8-2 win against Quebec Nordiques). Taylor had seven assists March 16, 1947, for the Detroit Red Wings in a 10-6 win against the Black Hawks. ... Draisaitl is the fourth Oilers player to have six assists in one game (Gretzky: Dec. 20, 1985, and April 9, 1987; Paul Coffey: March 14, 1986; and Mark Messier: Jan. 4, 1984). ... It was the third game Draisaitl and McDavid each scored at least five points. Each had five points (Draisaitl: four goals, one assist; McDavid: one goal, four assists) in an 8-3 win at the Nashville Predators on March 2, 2020. Draisaitl had five assists, and McDavid scored six points (three goals, three assists) in a 6-2 win against the Colorado Avalanche on Nov. 14, 2019. ... Tippett said defenseman Ethan Bear is day to day after sustaining an undisclosed injury in a 4-3 overtime win against the Toronto Maple Leafs on Saturday.