The teams will play here again Wednesday and Thursday.
"We got some guys that maybe are taking for granted positions in the National Hockey League," Ottawa coach D.J. Smith said. "We've got to find the right combination and we've got to give some other guys opportunity to see if they want to play a little harder than some of the guys that are playing now."
Sutter scored on a backhand shot to give the Canucks a 1-0 lead at 9:31 of the first period. He made it 4-1 with a shorthanded goal at 17:44 of the second after Demko made a glove save against Artem Anisimov in the slot.
Sutter, who started the season as a right wing on the fourth line before moving up to center the third line for a 5-2 loss against the Montreal Canadiens on Saturday, completed the hat trick on a breakaway with 54 seconds left in the third period.
"Anytime someone scores a hat trick, it's always a good feeling," Travis Green said. "But obviously in this scenario, a guy that doesn't get a lot of recognition for offense, you feel good for 'Sutts.'"
Tyler Motte made it 2-0 at 14:08 of the first after a turnover by Senators defenseman Thomas Chabot in front of his own net.
Demko, who has alternated starts with Canucks goalie Braden Holtby, saved two breakaways before the end of the first period. He got enough of Chris Tierney's shot with his glove that it hit the crossbar at 17:07, then denied Connor Brown at 19:37.
"That was something I really wanted to focus on as I kept getting in the games here is timely saves," Demko said. "Making sure that when they do get chances in situations like that, I can come up big and kind of give the team a chance to pull away even farther."
Watson cut it to 2-1 with a screened deflection that hit Demko in the mask and bounced in at 11:58 of the second period, but Vancouver restored its two-goal lead 30 seconds later. Nils Hoglander chipped the puck into the Senators zone, then dove headfirst to sweep it across to Tanner Pearson to make it 3-1 at 12:28.
Smith said he considered pulling Murray after the second period for a second straight start. Murray allowed four goals on 26 shots in a 4-1 loss to the Winnipeg Jets on Jan. 21.
"Certainly he didn't have a very good game, but he's got to work through it and find a way to battle for us there," Smith said. "He's no different than any other player and he's got to find his groove here."
Quinn Hughes scored his first goal of the season on a rebound to give the Canucks a 5-1 lead at 12:12, and Juolevi scored at 15:50 on a screened point shot to make it 6-1.