Jake Sanderson took a wrist shot from the left point and Batherson tipped it into the net from in front to give Ottawa a 3-2 lead.
Nick Cousins and Shane Pinto also scored, and Linus Ullmark made 24 saves for the Senators (10-6-4), who have won two of three and have points in eight of their past nine (5-1-3).
Beckett Sennecke and Mason McTavish scored for the Ducks (13-7-1), who had won six straight at home, including a 4-3 victory against the Boston Bruins on Wednesday. Petr Mrazek made 22 saves.
Cousins gave Ottawa a 1-0 lead at 16:39 of the first period on the rush, scoring on a one-timer from above the hash marks off a backhanded pass from Nick Jensen.
The Ducks scored twice in 1:26 of the second period to move ahead 2-1.
Sennecke tied it 1-1 at 13:08 off a feed from Cutter Gauthier.
Leo Carlsson passed the puck into the middle to Gauthier, who whiffed on a shot attempt, but the puck continued through the legs of Ottawa defenseman Artem Zub. Gauthier then stepped around Zub and backhanded a centering pass to Sennecke, who scored from the opposite post.
McTavish gave Anaheim a 2-1 lead at 14:34, finishing a feed from Chris Kreider on a 2-on-1 break.
Pinto’s power-play goal tied it 2-2 with 58 seconds left in the second. He scored from in close with six seconds left on the man-advantage after Mrazek missed a poke check.
Stephen Halliday, playing in his first NHL game, earned the primary assist on the goal.
