Patrick Maroon also scored for the Ducks, who are on their longest road trip of the season, playing eight games in 15 days. They lost on their first two stops, including a 4-1 defeat to Montreal on Thursday night.
"Our guys did a great job responding and getting back to the hockey that we like to play," Getzlaf said. "After back-to-back games you can't ask for anything else. Our guys did a great job parking (Thursday's) loss and focusing on this one."
Ottawa struggled all night with puck possession and making passes, making 16 giveaways to the Ducks' two.
"They didn't give us a lot of time and space to do anything and they were, I thought, for the most part better than we were," Senators coach Paul MacLean said. "We turned over pucks in the first period and we turned over pucks all night long."
Focus, or lack thereof, was an issue for the Senators as both Anaheim goals were a result of turnovers.
"It's a game of mistakes," Senators goalie Craig Anderson said. "They made mistakes also, but we didn't capitalize. When we had our opportunities, their goalie made some good saves or we missed our chances."
The Senators' best period was the third, but Andersen, who was making his first start for Anaheim, stopped all 12 shots he faced.
"I just want to build on this," Andersen said. "It was fun. It was nice to get a win."
Anderson made a couple of great saves late in the third to give the Senators a chance in the final minute with the extra man, but Ottawa was unable to score.
Maroon opened the scoring at 7:35 of the first period when he took a pass from Corey Perry and beat Anderson with a wrist shot.
A communication breakdown between defenseman Erik Karlsson and Anderson led to the Ducks second goal. Karlsson took the puck behind Ottawa's net but mishandled it, allowing Perry to grab it and put it out front. Karlsson again struggled to clear it and Getzlaf jumped on the puck and buried it.
"I don't think we were there from the start," Karlsson said. "We caught a couple of really bad breaks and we're down two goals. We're running up hill the whole game."
The Senators cut the lead in half midway through the second on Zibanejad's power-play goal, which came as a result of some great work by Cory Conacher, who took a beating in the crease to create a screen.
Zibanejad, who was recalled Tuesday, now has a goal and an assist in two games and was rewarded for his effort on the night as he saw time on the top line.
"It's nice to get that confidence up and be able to contribute to the team with goals and good play, but it's a tough loss," Zibanejad said.
Ottawa then took three straight minor penalties, but the Ducks' struggling power play couldn't convert.
"Those (penalties) are Duracell drainers for sure," MacLean said. "The opposition put us under some pressure again and forced us to take penalties. That's what good teams do to you and that's what speed does to you."
The Senators had a great opportunity to tie the game early in the third with the man advantage, but Clarke MacArthur, who is still looking for his first of the season, wasn't able to bury a loose puck.
This was the second and final meeting between the teams this season.