Charlie McAvoy picked up a loose puck in the left corner and skated all the way across the zone before sliding a shot on net from along the goal line. Linus Ullmark made the initial save, but the rebound sat near the right post, where Zacha jammed it in.
Morgan Geekie and Sean Kuraly also scored, Andrew Peeke had two assists, and Joonas Korpisalo made 20 saves for the Bruins (9-7-0).
Claude Giroux had a goal and an assist, Michael Amadio scored, and Ullmark made 22 saves for the Senators (6-5-3), who had not played since a 4-3 overtime loss at the Montreal Canadiens on Saturday.
Amadio gave the Senators a 1-0 lead at 5:42 of the first period. Shane Pinto took a short pass from Giroux at the offensive blue line, skated in on a 2-on-1 and passed across to Amadio, who finished glove side with a quick wrist shot from the bottom of the right circle.
Geekie tied it 1-1 at 1:22 of the second period. He jammed in a rebound at the left post after Peeke's slap shot from the top of right circle went under Ullmark's blocker arm.
The play happened after Geekie helped the Bruins maintain possession with an aggressive forecheck.
Kuraly put the Bruins in front 2-1 at 16:03. Tanner Jeannot controlled the puck along the right boards and quickly passed to Kuraly, who roofed a wrist shot over Ullmark's glove and under the crossbar.
Giroux tied it 2-2 at 11:52 of the third period. He scored one second after a power play expired with a shot from the left circle that trickled five-hole on Korpisalo through a screen.
