Chabot gave the Senators a 1-0 lead at 11:32 of the first period. Koskinen made the initial save, but the puck deflected up into the air and the goalie accidentally knocked the puck in off his blocker.
McDavid took a stretch pass from Evan Bouchard and scored with a partial slap shot off the rush to tie it 1-1 at 12:17.
"I don't know if we played well enough through 60 minutes to deserve a win, in my opinion," Oilers forward Derek Ryan said. "But good on us to battle through and stick with it. They're a tough team to play against. They play hard, they play the right way. They keep a lot of pucks and bodies away from their net, and their goaltender was awesome, too."
Nicholas Paul gathered a rebound and put a backhand top shelf on the power play to make it 2-1 at 17:09 of the second period.
"I thought [Paul] was the best player on the ice for us," Smith said. "There's very few people in the world who can skate with McDavid, especially a forward [skating] back, and he did it in overtime, and with Draisaitl when he had to. He killed penalties, scored. I don't know what else he's got to do, but you know, he's playing with confidence and he's giving us a chance."