Judd Caulfield had two goals and an assist, Leo Carlsson had three assists and Tristan Luneau had two assists for the Ducks (6-7-1), who had lost seven of eight (1-6-1) and trailed 3-0 after the first period against the Senators.
Laurent Brossoit was recalled from San Diego of the American Hockey League on Saturday and made 19 saves in his first start for Anaheim.
It was just the second NHL game in the past 2 1/2 years for Brossoit, who was given the opportunity after Lukas Dostal allowed a combined 10 goals on 65 shots (.846) in his past two starts, and Ville Husso gave up 15 goals on 88 shots (.830) in his past three starts.
Claude Giroux had a goal and an assist for Ottawa (9-6-1), which was coming off a 5-1 win at the San Jose Sharks on Saturday. Jonas Johansson made 27 saves.
After Ottawa took a 3-0 lead into the second period, Gauthier took advantage of a turnover in the Ottawa zone and scored from in close to cut it to 3-1 at 1:35 of the period.
Caulfield won a battle for a loose puck in the crease and pushed it across the goal line to make it 3-2 at 3:33.
After killing three penalties, including a 19-second 5-on-3, the Ducks went on their first power play and scored with three seconds left on the man-advantage on Caulfield’s netfront tip of Luneau’s shot from the point with 42 seconds remaining in the period to tie the game 3-3.
Gauthier scored with a one-timer from below the right circle, going short side with a sharp-angled shot on a 5-on-3 power play, giving Anaheim a 4-3 lead at 1:50 of the third period.
Gauthier then scored on the ensuing 5-on-4 from nearly the same spot to make it 5-3 at 2:26.
Roger McQueen scored the fourth power-play goal for the Ducks with a snap shot from the left dot to make it 6-3 at 15:19.
Brossoit made his first two saves on an early penalty kill, but gave up a goal on the third shot when Philip Tomasino tipped Thomas Chabot’s shot from the left face-off circle for a 1-0 lead at 6:00 of the first period.
Giroux scored from the right circle off a rush to make it 2-0 at 7:02, and Michael Amadio found a gap in the Anaheim defense and scored on a breakaway to make it 3-0 at 17:37 of the first.
Ottawa scored on three of its first seven shots.
