New York opens the Stanley Cup Playoffs against one of the Pittsburgh Penguins, Washington Capitals, Detroit Red Wings or Philadelphia Flyers, who all remain in contention for the second wild card from the Eastern Conference.
The Rangers went 26-7-1 in their last 34 games.
"We did a good job of just staying focused and staying consistent and playing hard inside of those games, trying to do the right things," Laviolette said. "Down the stretch we were good. We stayed pretty solid with our game. That's good because now you're heading into why you did all that work. Now it's the first round of the playoffs."
Joonas Korpisalo made 30 saves for the Senators (36-41-4), who had won two in a row.
"The unfortunate part is we gave them the first two goals," Ottawa coach Jacques Martin said. "We talked about it this morning, puck management. The first goal, turnover. The second goal, a short-handed goal. Take those two goals aside, it's a pretty good game.
"They've got a good team and I thought we battled hard, but when you play these good teams, you can't afford to give them freebies."
The Senators end their season at the Boston Bruins on Tuesday.
"One left," Ottawa forward Drake Batherson said. "We would have liked to win the last two, but look forward to [Tuesday] against another good team and hopefully finish on a good note."
Jack Roslovic gave the Rangers a 1-0 lead at 5:55 of the first period after scoring on a 2-on-1 with Kreider, an odd-man rush he created by forcing the Senators into a turnover at the defensive blue line.
Fox's short-handed goal off a 2-on-1 with Kreider made it 2-0 at 8:58 of the second period. Mika Zibanejad started the rush and Kreider joined, setting up a give-and-go with Fox. Kreider's pass eluded Thomas Chabot and Fox knocked it past Korpisalo.
"I thought the team played well," Laviolette said. "I thought we just competed hard. Ottawa played hard, they were ready at the start and they competed for 60 minutes, so it wasn't a layup by any stretch, but over the course of time we were able to keep chipping away at it."
Panarin made it 3-0 at 4:34 of the third period off a deflection from between the circles of Ryan Lindgren's shot from the point.
Panarin ended the regular season with a 13-game point streak (11 goals, 15 assists). He had 18 shot attempts Monday.
"I feel like I had the chance to hit 50 [goals]," Panarin said.