The 26-year-old’s first of the night was his 100th career goal.
Ottawa (13-13-2) dominated the game from the start and capitalized on its opportunities.
The Senators closed out its four-game homestand with a 3-1-0 record.
The Ducks (10-13-4) have lost four in a row and their first on the road in regulation since Oct. 31.
Noah Gregor opened the scoring for the Senators at 2:55 scoring on their first shot of the game.
The Senators then capitalized on a lengthy two-man advantage when Batherson scored his first. The puck disappeared under a sprawling John Gibson, who made 29 saves. It was declared a goal upon review.
Batherson made it 3-0 with his second power-play goal of the night and completed the hat trick midway through the second.
He also picked up an assist on Brady Tkachuk’s power-play goal to make it 5-0.
Cutter Gauthier spoiled Linus Ullmark’s shutout bid with his fourth of the season. Ullmark faced 31 shots.
Leo Carlsson returned to the Ducks lineup after missing six games.
Senators: Special teams were the difference for Ottawa going 3-for-5 on the power play and going a perfect 5-for-5 on the penalty kill.
Ducks: By the time Anaheim found their game legs, the Ducks trailed 3-0.
Already killing a holding penalty, the Ducks took a delay of game minor to give Ottawa a two-man advantage for almost two minutes. The Senators capitalized for a 2-0 lead.
The Ducks have struggled at home (5-9-1), but coming into the game were 4-0-2 in their last six on the road.
The Senators are in Carolina to face the Hurricanes on Friday. The Ducks head to Toronto to meet the Maple Leafs on Thursday.