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). 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.
“We got away from being aggressive, and we did, and I thought we got very selfish with the puck,” Blue Jackets coach Rick Bowness said. “Some of these guys, they've got a lot to learn about how to play in this League at this time of year.
“It gets harder and harder and harder, and we're going to keep reminding them and reminding them every day how hard it is to win at this time of the year, and you just can't get away. I hate it when we play on our heels, and we were back a little bit. Give them credit. They started coming but there's a lot to be learned from some of these guys, and they better damn well start listening.”
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.
“They're going to come and push and play well and press a little bit, but it's up to us, no matter what happens, just to stay on it,” Coyle said. “We can't be turning the puck over like that and giving them easy transitions.”
NOTES: Zacha had the fourth-latest game-tying goal over the past 30 years for Boston. ... The Bruins had their ninth three-goal, third-period comeback in franchise history and first since March 13, 2018 (6-4 win at Carolina). ... McAcvoy set a new career high for points in a season with 57 (11 goals, 46 assists), besting his previous high of 56 he set during the 2021-22 season. ... Boston defenseman Mason Lohrei did not play because of an upper-body injury. ... Jenner played his 800th NHL game. ... Blue Jackets forward Mathieu Olivier left the game in the second period with an upper-body injury and will be evaluated on Monday.