Charlie McAvoy made it 3-1 at 6:29 of the third when his wrist shot from the blue line squeaked through a screened Jet Greaves.
Zacha brought Boston to within 3-2 with a power-play goal at 8:43. McAvoy sent a shot from the left point that Zacha deflected in the left circle over Greaves' glove and in off the right post.
Zacha scored his second goal while on the power play at 19:49, lifting a loose puck past Greaves to the blocker side during a 6-on-4 advantage with Jeremy Swayman pulled for the extra attacker.
Victor Arvidsson had three assists, and McAvoy also had an assist for the Bruins (42-24-8), who have won five of their past six.
Swayman made 21 saves in his second of back-to-back starts. He made 31 saves in a 6-3 win against the Minnesota Wild on Saturday.
Arvidsson and Fraser Minten scored in the shootout, and Swayman stopped Adam Fantilli and Kirill Marchenko to clinch the win.
David Pastrnak had his point streak end at 12 games (seven goals, 13 assists).
Mason Marchment had a goal and an assist, and Boone Jenner and Charlie Coyle scored for the Blue Jackets (38-24-12), who have lost four of five (1-3-1). Kirill Marchenko had two assists, and Greaves made 35 saves.
Columbus also allowed a go-ahead goal with 1:25 left in a 3-2 loss to the San Jose Sharks on Saturday.
Jenner gave the Blue Jackets a 1-0 lead at 6:17 of the first period. Conor Garland forced a turnover in the defensive zone, skated down the length of the ice and fed a pass to Jenner, who was trailing the rush. Jenner then glided into the slot and buried a wrist shot low to the blocker side.
Marchment made it 2-0 just 1:28 later at 7:45, tipping Ivan Provorov's point shot between Swayman's pads from in front.
Coyle's power-play goal at 19:32 increased the lead to 3-0. Marchenko sent a cross-ice pass from the left boards to Coyle in the right face-off circle, where he beat Swayman's glove with a snap shot into the top right corner.
Blue Jackets forward Mathieu Olivier left the game in the second period with an upper-body injury.
