The 20-year-old Lehner, appearing in his 11th career game and second of the season, turned aside 17 shots in the third period for the Senators, who pulled to within a point of the Bruins atop the Northeast Division.
Lehner was playing in place of injured regular goalie Craig Anderson.
Erik Karlsson, who leads all NHL defensemen with 66 points, notched the game's only goal as Ottawa improved to 6-1 in its last seven games.
Tim Thomas turned aside 38-of-39 shots for Boston, who were saddled with their seventh shutout of the season and fifth of the month.
Celebrity Families of 2014 [PHOTOS]