It was the second consecutive three-point game for Batherson, who also had two goals and an assist in a 7-1 win at the Washington Capitals on Saturday.
Jake Sanderson had three assists, and Fabian Zetterlund had a goal and an assist for the Senators (5-4-1), who have won three straight and are 3-0-1 in their past four games. Leevi Merilainen made 26 saves for his first win of the season; he was recalled from a conditioning stint with Belleville of the American Hockey League on Thursday.
Morgan Geekie and Viktor Arvidsson each scored, and Jeremy Swayman made 17 saves for the Bruins (4-7-0), who have lost seven of their past eight.
Ottawa was 4-for-5 on the power play; Boston was 0-for-1.
Geekie gave the Bruins a 1-0 lead at 3:06 of the first period. He intercepted a Zetterlund pass attempt near the Senators’ blue line and beat Merilainen glove side with a wrist shot from the top of the left face-off circle.
Batherson swept in a Ridly Greig rebound at the edge of the crease on a power play to tie it 1-1 at 10:25.
Claude Giroux redirected a Michael Amadio centering pass to put the Senators up 2-1 at 1:08 of the second period.
Batherson scored his second goal of the game to make it 3-1 at 14:44 when he took a centering pass from Zetterlund and beat Swayman blocker side with a wrist shot from the slot.
Stutzle pushed it to 4-1 13 seconds into the third period, putting a wrist shot past Swayman’s glove from the top of the left face-off circle on a power play. He scored his second power-play goal of the period when he tipped in a Sanderson point shot for a 5-1 advantage at 9:33.
Nick Cousins buried a Stutzle rebound from in front to extend the lead to 6-1 at 12:22.
Zetterlund made it 7-1 at 13:04, scoring his first goal of the season with a long-range one-timer on a power play.
Arvidsson beat a heavily screened Merilainen from distance at 19:50 for the 7-2 final.
