Brady Tkachuk had a goal and an assist, and Tim Stutzle had two assists for the Senators (13-13-2), who are 3-1-0 in their past four games. Linus Ullmark made 31 saves; he is 4-0-1 in his past five starts.
Cutter Gauthier scored, and John Gibson made 29 saves for the Ducks (10-13-4), who have lost four straight (0-3-1).
Ottawa was 3-for-5 on the power play; Anaheim was 0-for-5.
Noah Gregor scored on a pass from Zack Ostapchuk in tight to give the Senators a 1-0 lead at 2:55 of the first period.
Batherson made it 2-0 at 11:15 on a power play. His one-timer from the bottom of the left face-off circle snuck under Gibson's left pad and video review was needed to confirm that the puck crossed the goal line.
Batherson scored his second power-play goal of the period to push it to 3-0 at 18:25. His centering pass from the goal line to the left side of the net went in off Cam Fowler's skate.
He then completed the hat trick to make it 4-0 at 10:30 of the second period when his turnaround wrist shot from the left point redirected in off Fowler's stick.
Tkachuk batted in a saucer pass from Batherson at the edge of the crease on the power play to make it 5-0 at 8:58 of the third.
Gauthier tipped a Mason McTavish shot for the 5-1 final at 12:42.