Draisaitl one-timed a cross-ice pass from McDavid on the power play to give the Oilers a 1-0 lead at 12:18 of the first period.
"It's hard to defend, especially him, because he's the best passer in the game," Draisaitl said of his chemistry with McDavid. "He'll find those little triangles, those little seams, and it's my job to find an opening and make it easy for him to get it over there. And then it's just about being ready and trying to bear down and put it in."
Senators defenseman Thomas Chabot picked up his rebound, skated around the net and passed in front to Norris, who tapped it in five-hole to tie it 1-1 25 seconds into the second period.
Draisaitl scored from below the goal line, one-timing a pass from McDavid to make it 2-1 at 17:26.
"That was obviously a shot that only a few guys in the world can make, and he's one of them," McDavid said. "He likes shooting from there, I think. He's scored a few times from there."
Brown scored with a wrist shot from the slot to tie it 2-2 at 1:02 of the third period. It was Brown's fifth straight game with a goal after scoring one in his previous 13.
"He's shooting it a lot more, that's for sure," Senators coach D.J. Smith said. "When you work hard, sometimes you earn a bit of confidence and some go in. He had been snake bitten there for a while, and then all of a sudden everything he's shooting is going in."
NOTES: Hogberg had been out with a lower-body injury. "He made some saves when he had to make them," Smith said. "He came back, he looked confident, he did what he had to do for us." ... The Oilers have outscored the Senators 38-17 this season.