The Sabres are 0-15-2 since Feb. 23 and extended their NHL shootout-era record for the longest stretch without a victory. The shootout was implemented in the 2005-06 season, eliminating ties.
Linus Ullmark made 33 saves in his return after missing 15 games because of a lower-body injury for Buffalo (6-23-4).
"We obviously played a good game, a good hockey game," Sabres forward Kyle Okposo said. "A couple bounces end up in the back of our net and I just didn't think we had enough looks in the third period there to really try and put them away and end the game. We've just got to find a way to keep pushing for offense.
"But it was a lot better without the puck, and I thought we did a good job to kind of limit their time and space and we did a lot of good things tonight, we just weren't able to get the W."
Boston (17-8-5) extended its point streak to four games (3-0-1).
The Bruins trailed 2-1 heading into the third period before Nick Ritchie tied it 2-2 at 5:22 and Craig Smith scored at 16:10 for a 3-2 lead.
Ritchie scored on a tap-in after Charlie McAvoy circled the net and passed to the front. The puck deflected off Buffalo defenseman Rasmus Ristolainen to Ritchie.
"I was just trying to use kind of my momentum to just get skating. I know they're a man-on-man team, so I was trying to get a step," McAvoy said. "I was actually looking for [Smith] through a seam there, and then we were fortunate enough to get a bounce. But when guys are going to the net all game and working hard to get to those dirty areas, it's nice to see them get rewarded."