Morgan Geekie scored the only goal for the Bruins (13-11-0), who have lost three of four. Jeremy Swayman made 28 saves.
"They tried everything they possibly could. We just found ourselves down a couple of goals against a hot goalie, too," Boston coach Marco Sturm said. "[We] probably didn't do a good enough job in front of him. It was just unfortunate to leave points here."
Mukhamadullin scored his first goal of the season to give the Sharks a 1-0 lead at 15:53 of the first period. Mario Ferraro slid a pass to the right point for Mukhamadullin, whose wrist shot from the right circle deflected off Bruins forward Michael Eyssimont's stick and over Swayman's glove.
Celebrini made it 2-0 with a power-play goal at 11:45 of the second period. Dmitry Orlov faked a slap shot at the point and instead slid a pass to Celebrini at the left wing, where he scored with a snap shot that beat Swayman glove side.
Celebrini extended his point streak to five games (four goals, four assists).
"We had plenty of chances, and I thought we did a better job at least gaining momentum, not just going out there and whacking the puck around," Celebrini said. "We strung some chances together, which is nice. It kind of gives your group life. That was just an amazing screen by [Alexander Wennberg]."
Geekie cut the lead to 2-1 at 10:02 of the third period. David Pastrnak circled the net and fed a cross-crease pass to Geekie, who put a wrist shot past Askarov's right pad.
It was Geekie's 17th goal of the season, which is tied with Colorado Avalanche forward Nathan MacKinnon for the most in the NHL.
"That play has worked for us before," Geekie said. "[I] just try to be in the right spot and time it right. Fortunately, it worked out."