"After our last performance (7-3 loss to the Pittsburgh Penguins on Tuesday), we wanted to come in here and make sure that we didn't lay an egg here on home ice," Anderson said. "Right from the get go, I thought we played hard, played together, played as a group and got rewarded for our play."
Mathew Barzal had a goal and two assists, and Semyon Varlamov made 25 saves for the Islanders (35-23-8), who are 0-3-2 in their past five games and 2-7-2 in their past 11.
"It's disappointing to lose this one," New York forward Jean-Gabriel Pageau said. "We need all the points right now, and we've got to find our game as fast as we can. I think we need more urgency in our game. So we're going to go back (to New York), refocus and get back at it. I mean, it's desperation time right now."
WATCH: [All Islanders vs. Senators highlights]
The Islanders lead the New York Rangers by two points for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
"It's tough, but that's what good teams do, they find a way," New York defenseman Ryan Pulock said. "We need to just bear down. We've just got to get the thinking out of our heads and just go to work and just be simple and just have some fun playing the game and get our swagger back and get back to work."
Brady Tkachuk scored his 20th of the season for the Senators (24-32-12), who have won three of their past four games.
"It's fun to play against the playoff teams, the elite teams on our side of the League," Ottawa forward Mikkel Boedker said. "We came out and we played hard and I think it was a good win. [Anderson] played well, so that was good to see."