Batherson also scored in regulation, Tim Stutzle had a pair of goals and Thomas Chabot also scored for Ottawa in this matchup of teams near the bottom of the Eastern Conference. Brady Tkachuk chipped in three assists, while Anton Forsberg made 37 saves.
Nolan Foote had a pair of goals for the Devils, whose skid extended to four games. Pavel Zacha and Yegor Sharangovich also scored.
Mackenzie Blackwood, making his first start since Jan. 19, stopped 29 shots for the Devils.
Stutzle had the crowd of 13,101 chanting his name when he beat Reilly Walsh in a foot race for the first short-handed goal of his career. Less than a minute later, Zacha beat Forsberg to cut Ottawa's lead to 4-3 at the seven-minute mark of the third.
The Devils completed the comeback when Zarangovich was given too much time and space in close, scoring to force the extra period.
Batherson gave the Senators a 2-0 lead 11 seconds into the second period with his 16th goal of the season.
The Devils got on the board when Fabian Zetterlund made a nice pass to Foote for his first of the season.
A few minutes later, the Senators made it 3-1 with their second power-play goal as Stutzle jumped on a Tkachuk rebound.
Foote scored his second of the game with 5.2 seconds left in the period, beating Ottawa's Mark Kastelic to a rebound at the side of the net.
The Senators opened the scoring with 16.9 seconds left in the first period when Tkachuk made a cross-crease pass to Chabot, who knocked in his seventh of the season.
NOTES: The Senators will finish the season without Matt Murray, Connor Brown, Colin White and Mathieu Joseph. ... New Jersey recalled Reilly Walsh from Utica of the American Hockey League. ... The Devils' Nico Hischier missed a second straight game with a non-COVID-19 illness.
Devils: At Carolina on Thursday night.
Senators: Host Florida on Thursday night.
More AP NHL: https://apnews.com/hub/nhl and https://twitter.com/AP-Sports
Copyright 2022 STATS LLC and Associated Press. Any commercial use or distribution without the express written consent of STATS LLC and Associated Press is strictly prohibited.