Vlasic stole the puck off the goal line and denied Bruins forward Chris Wagner's scoring chance in the first period.
Bruins defenseman Charlie McAvoy fired a shot from the point that deflected by Jones. The puck was sliding in for a sure goal, when Vlasic dove into the net and attempted to knock the puck away.
Vlasic swatted the puck out of the crease prior to it crossing the goal line. Officials reviewed the play and ruled that the puck never crossed the line.
The Bruins (35-17-8) defeated the Sharks 6-5 in overtime. McAvoy scored the game-winner in the extra period for Boston's sixth straight victory.
Center Joe Thornton led San Jose with his fifth career hat trick.
San Jose (35-17-8) travels to Pittsburgh for a game against the Penguins on Thursday night. The Bruins head west to play the Vegas Golden Knights on Wednesday.