Nygard tied it 2-2 on the power play at 15:56 when he tipped a point shot from Nurse.
"We didn't have the right mindset when we came out," Oilers coach Dave Tippett said. "Early on, I think that we thought that we had a couple of guys coming back into the lineup and that it would just be free-wheeling and passing the puck into the net. When you don't compete the right way, you don't stomp on loose pucks, you don't take care of the puck, it ends up coming back at you. It came back at us two times in the first period, and we got behind."
Edmonton's Leon Draisaitl hit the goal post on a backhand with 6:54 left in the third period.
Draisaitl, who leads the NHL with 53 points (19 goals, 34 assists), and Oilers center Connor McDavid, who is second with 52 (19 goals, 33 assists), were held without a point. It was the fourth game this season that neither had a point.
"It was a beautiful victory here, especially because of the character we showed to get it," Krueger said. "We came out with a really good start, and until about the eight-minute mark of the second period, we were on track for a solid game. We let it slip, but I loved the way the guys recovered in the third period."