The Senators felt they showed some of that character in the first two periods, when they allowed one goal on 22 shots, an improvement on how they played defensively in their three previous games.
Andersson gave the Rangers a 2-1 lead at 3:26 of the third period, when the rebound of Ryan Strome's shot hit off his backside and went into the net. It was his second goal in 18 NHL games.
Ottawa coach Guy Boucher challenged for goalie interference by Andersson, but the call on the ice of good goal was upheld by video review.
"A goal is a goal," Andersson said. "Definitely not the prettiest one, but I'll still take it."
Kreider made it 3-1 at 8:18, scoring off a 2-on-1 with Filip Chytil that started because Senators defenseman Cody Ceci pinched in too low and Ottawa didn't have the support of a forward to stay higher in the zone to defend if the puck popped out, which it did.
"The goal at the beginning of the third period, that's fine, it's only one goal," Boucher said. "We always come back. We've got the capacity to do so. But again, it's the extra goal that hurt us like all of these games we've seen because we're too eager to get it right away, we're not patient with the result. That's the maturity we have to build."
Stone cut the Rangers lead to 3-2 with a 6-on-5 goal at 17:17, Ottawa's sixth shot on goal in a span of 1:51, but Zibanejad made it 4-2 with an empty-net goal at 18:21.
"One of the things we talked about in between the second and third was I thought the team that played the most honest hockey was going to win the hockey game," Rangers coach David Quinn said. "I didn't think there was a lot of honest hockey from our end in the first two periods. From the drop of the puck in the third, we were paying attention to detail, we weren't getting ahead of ourselves, and we showed all the things you need to show to play winning hockey.
"After we made it 3-1, I thought we reverted back, and I thought thank God for our goalie because that game could have been 3-3 in a hurry."
Staal gave New York a 1-0 lead at 10:55 of the first period.
The Senators tied it 1-1 2:08 later when Stone scored his first. Quinn challenged for goalie interference by Colin White, but the call on the ice of good goal was upheld by video review.
"It happened so quickly when he got to the rebound, so I think it was the right call," Lundqvist said.