The Sabres stayed patient as they protected a one-goal lead through 38 minutes and finished the night with advantages in shots and scoring chances, but the Bruins capitalized on late chances to claim a 3-1 victory inside KeyBank Center on Saturday.
Tage Thompson scored a highlight-reel, shorthanded goal to extend his point streak to four games. Anderson made 27 saves.
The Bruins scored three unanswered goals after trailing 1-0 for most of the first two periods. Patrice Bergeron scored the tying goal with 1:49 remaining in the second period and added an insurance goal late in the third period. Jakub Zboril scored the winner with 7:29 remaining.
The Sabres are winless in their last five games. The stretch opened with tightly contested road losses to two Eastern Conference contenders in Carolina and Tampa Bay, followed by home losses to the NHL's current top two teams in Vegas and Boston.
The Bruins entered Saturday ranked first in the NHL in goals scored per game, second in goals allowed per game, and first on the penalty kill. Their 24 points in the standings led the Eastern Conference.
"It pisses them off," Sabres coach Don Granato said when asked about what the players will take from the last two weekends. "That's a really good thing for us, is we brought in competitive people. We know they're young, but we brought in competitive people for that reason.
"When this stuff happens, they don't like it. They want to fix it. And I think the silver lining is they know they can fix it. We need to keep gaining the experience to make the know how knowledge."
Thompson echoed his coach, recognizing the positives on Saturday while remaining adamant that the team is hungry for more.
"You want to win every game," he said. "We don't come into games just hoping we win. We're going out there to try to outplay them and I think we did for the most part. But they're a good hockey team. You give them an inch, they're going to take a mile. That's kind of what happened tonight."