McDavid has eight goals this season, tied for the league lead with Vancouver's Brock Boeser, and leads the points race with 22 - one ahead of Draisaitl.
Draisaitl was one assist off the NHL record shared by Edmonton great Wayne Gretzky (accomplished three times in the 1980s) and Detroit's Billy Taylor (in 1947).
''I was not aware of that. It's not something I pay too much attention to,'' Draisaitl said.
The German forward leads the NHL in assists with 15, one more than McDavid.
Dominic Kahun, James Neal, Ryan Nugent-Hopkins, Tyson Barrie, Darnell Nurse and Kailer Yamamoto also scored for the Oilers. Stuart Skinner made 33 saves in his NHL debut, handing Ottawa its eighth straight defeat.
''It was nice that we got up a couple and the guys in front of me were playing really good tonight,'' Skinner said. ''Obviously, they potted out eight goals. That obviously helped.''
The teams will complete the two-game set in Edmonton on Tuesday night.
It took eight seconds for the Oilers to score. Off a faceoff win by Draisaitl in the Senators zone, Kahun took a pass from his center and fired a shot toward the net. The puck deflected off Ottawa forward Josh Norris' stick and past goaltender Matt Murray.
McDavid scored on a power play 42 seconds into the second period.
''Their big guys took us apart tonight,'' Senators coach D.J. Smith said.
Colin White, Brady Tkachuk, Drake Batherson, Tim Stutzle and Austin Watson scored for Ottawa.
Murray allowed three goals on nine shots before being pulled in the first period. Marcus Hogberg stopped 17 of 22 shots the rest of the way.
Edmonton (5-6-0) has back-to-back wins for the first time this season. Meanwhile, the Senators (1-7-1) have the fewest points in the league with three - every other team has at least six.
Smith called his team ''fragile'' after the loss and lamented taking ''questionable'' penalties, resulting in four power-play goals allowed.
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