Chris Kreider had two goals and an assist in the first period to help the Rangers get off to a quick start. Dan Boyle, Mats Zuccarello and Tanner Glass also scored for New York (47-19-7), which had an opportunity to clinch the playoff berth with a win because the Boston Bruins lost 3-2 in overtime to the Anaheim Ducks.
It was the first regulation loss in the 17-game NHL career of Ottawa goalie Andrew Hammond, who started 14-0-1.
Curtis Lazar scored for the Senators (37-25-11), who hung on to the second wild card into playoffs in the Eastern Conference with the Bruins' overtime loss. Ottawa and Boston each has 85 points, but the Senators have played one fewer game.
The game was a good bounce-back performance for the Rangers, who lost 4-2 to the Los Angeles Kings on Tuesday in New York.
"It's definitely something we talked about," said Kreider, who has 20 goals. "Lately, our starts have been pretty good, but after our start the other night, we kind of dropped off a bit and didn't play Rangers hockey. It's good to see a consistent effort from start to finish.
"I'm happy we clinched, and now we'll try and get home ice."
The Senators lost in regulation for the third time in their past 22 games (17-3-2). Hammond was pulled in the second period after he gave up five goals on 22 shots.
"They came in and did exactly what they wanted to do," Hammond said. "I thought they set the tone from the start. They play such a system; if you're not ready to play, you're going to get exposed, and I thought we did tonight."
Asked how he would respond to his first NHL regulation loss, Hammond said, "You just have to show up tomorrow and put your big-boy boots on, and go back to work. It's been long enough now that I have confidence; I know I can play at this level. It's just a matter of coming in tomorrow and putting the work in again, and just being ready for the next game."
Rangers goaltender Cam Talbot made 23 saves for the victory. He is 16-4-3 since taking over the starter's role in early February after an injury to Henrik Lundqvist, who is expected to play this weekend after a vascular injury in his neck; he backed up Talbot on Thursday.
Talbot (20-8-4) is the first Rangers goalie other than Lundqvist to win 20 games since Mike Richter in 2001-02.
Zuccarello scored his 14th of the season to put the Rangers up 4-1 at 1:42 of the second period, and then New York's penalty-killers took over.
The Senators had a great opportunity to get back in the game when the Rangers took three straight penalties beginning at 10:02 of the second period. The first two were assessed to Rick Nash, and Glass was called for slashing with 34 seconds left in Nash's second penalty.
The Rangers killed off all three shorthanded situations, and Glass came out of the penalty box, took a pass from Kevin Hayes and scored his first goal of the season to make it 5-1 at 16:02 of the second.
"They got three quick (power plays) at the end of the second there that could have put them back in the game, but our penalty-killing stood tall," Vigneault said. "Our guys blocked the right shots, blocked the right lanes."
Senators coach Dave Cameron pulled Hammond shortly after Glass' goal. Chris Driedger, who was recalled from Evansville of the ECHL last week, made 10 saves in his NHL debut.
Kreider was flying to start the game, when the Rangers took a 3-1 lead and made Hammond look quite ordinary in the process.
"It's visibly noticeable when (Kreider's) going the way he is going," said Rangers center Derek Stepan, who assisted on Kreider's goals. "He's all over pucks. He's the fastest guy on the ice. He's playing a real strong game. I thought he did a really good job tonight of doing that early."
Kreider scored on a dash down the left wing at 12:38 to give the Rangers the lead, but the Senators tied it 19 seconds later on Lazar's fifth goal. New York defenseman Keith Yandle couldn't handle a bouncing puck, and Lazar broke in and scored to the glove side.
After Boyle gave the Rangers a 2-1 lead with a shot from the slot, Kreider scored a backbreaker with a weak goal on Hammond.
A shot by Stepan from the left wing hit Hammond, popped into the air and fell behind the Ottawa goalie in the crease. Kreider knocked in the loose puck with a minute to go in the first period.
Kreider said the Rangers didn't have a book on Hammond.
"We didn't. Like any goalie, hot or not, veteran or rookie, (get) pucks (on net)," he said. "You can't score if you don't shoot.
"We hadn't heard all that much (about Hammond). We heard they had been hot recently. We hadn't heard much about the goalie in particular. The only thing we had really heard was they were throwing hamburgers on the ice after games. That was the extent of it. Your approach doesn't change regardless of who you're playing. That's the professional mentality."
"As far as I understood quickly there, it was a gash," Vigneault said. "The puck cut him, and he was just getting stitched up. I don't think it's anything more than that."
The Rangers visit the Bruins on Saturday and host the Washington Capitals on Sunday.