Nurse scored 23 seconds later at 4:23 on a 2-on-1 rush with Leon Draisaitl to tie it 1-1.
"Anytime you lose, there is no satisfaction in this room, there are no moral victories," Nurse said. "We are not happy being 1-2 to start the year. We can say all we want, but we have got to come out and show it on the ice. We made a lot about the need to have a good start to the game, and I thought our start was better than the first two [games]."
Thompson gave the Sabres a 2-1 lead 44 seconds into the second period. He rounded Nurse on a rush down the right wing, cut back inside against Skinner and tucked the puck into the net.
"I was just driving with some speed down the wing and saw some open ice in the middle," Thompson said. "Once I got my backhand, I tried to bring it back to my forehand, I figured the goalie would be sliding, and it worked out."
Peterka extended the lead to 3-1 on a breakaway at 5:15 following an offensive zone giveaway by Draisaitl.
"In the second period, we made a couple of mistakes that ended up in the back of our net and we weren't able to outscore those mistakes," Oilers coach Jay Woodcroft said. "But certainly through period 1 and period 3, we liked what we saw."