"I thought the first period cost us the game. When you get down 2-0 on the road, it's tough to come back and win those games," Canucks coach Travis Green said. "I like that we came back and tied it, but you're chasing the game right from the get-go and their third goal is obviously a big goal.
"We get an unlucky bounce on the fourth goal where it goes off the linesman's skate and they go down on the 2-on-1. When you get down against a team like that and you're chasing it, you have to take a few chances and the third period played itself out."
Sedin scored at 1:46 of the second period on the power play to make it 2-1 on a tip in front after a shot from the point by Alexander Edler.
Sutter tied the game 2-2 at 8:56, converting a pass from Sven Baertschi on a 2-on-1 rush.
Puljujarvi gave Edmonton a 3-2 lead at 18:54 on a rebound after a shot from Adam Larsson.
"(Puljujarvi) played a tremendous game for us. I thought he played strong both ways," Oilers coach Todd McLellan said. "He was physical along the boards and won a lot of his battles and he looked confident, passing and shooting."
Puljujarvi set up Draisaitl on a 2-on-1 rush at 4:37 of the third period to give Edmonton a 4-2 lead.
"That third one they got is obviously huge at the end of the second, and in the third we gave up way too many odd-man rushes," Daniel Sedin said. "We can't start chasing the game. We have to play the same way, we have to get pucks deep. We know we're going to get a chance to score that third one, but we gave up way too many odd-man rushes."
Maroon scored into an empty net at 17:17 of the third to make it 5-2.
"I think we battled back real good in the second and they got that late goal," Canucks defenseman Alexander Edler said. "We gave them some odd-man rushes and we're chasing, trying to create offense, and I think when we're successful, we've been playing tight defensively and creating offense that way. They made some good plays and got some goals."