Lee gave New York a 1-0 lead on the power play at 17:35 of the first when he poked in the rebound of a shot from the slot by Nelson.
Nelson made it 2-0 at 7:23 of the third period. After Kyle Palmieri blocked a shot while playing without his stick, Ross Johnston moved the puck ahead to Nelson, who carried the puck down the right wing and scored from the right face-off circle.
"We just wanted to get on the attack, get on the offense," Nelson said. "I thought we did a pretty good job of that, of dictating more of the play. Whenever you get a goaltender fresh or not, you've got to press him and get in there. I thought we did a pretty good job of getting some pucks to the net."
Toews cut it to 2-1 at 10:19 when he redirected a shot by Caleb Jones for a power-play goal.
"I thought we came out a little bit flat," Jones said. "It was a 1-0 game going into the third, and unfortunately, they got that one, but we battled back and got that one on the power play and we couldn't find that other one. We're in all these hockey games, we've just got to find a way to start pulling them out.
"I think we're playing hard, we're playing within our structure. Obviously, we're going to keep trying to get better every day and improve little things, but we have to find a way to start winning these games. That's how you become a really good team, when you can win more of these games than lose them."