Carl Soderberg assisted on both of Fraser's goals and Tuukka Rask made 28 saves for the Bruins, who have won three of four. Brad Marchand and Dennis Seidenberg also scored for Boston.
Mark Stone scored for Ottawa with 28 seconds left in the first period and Mika Zibanejad added a goal for the Senators in the third.
The Senators never recovered after Boston scored three straight times on Fraser's goals in the second period and Seidenberg's early in the third.
Robin Lehner finished with 25 saves for Ottawa.
Fraser, who didn't have a point in his first four games this season, scored when a rebound came right to him with 8:46 left in the second. He beat Lehner on a high wrist shot 1:28 later to give the Bruins a 3-1 lead. It was more than enough offence for Boston, which held Ottawa to five shots in the first period.
Fraser had three career goals entering the game.
Marchand scored the game's first goal with 1:06 left in the first period. Patrice Bergeron assisted, winning a faceoff and slipping the puck behind him to Marchand for a shot that got through Lehner's pads and trickled over the goal line.
The Senators answered with a late goal of their own when Stone stole the puck from Seidenberg and beat Rask on a breakaway to tie it.
Seidenberg scored 2:08 into the third to give Boston a 4-1 lead.
NOTES: The Bruins held a moment of silence for former Boston Mayor Tom Menino, who died Thursday. That was followed by a brief slide show that concluded with a photo of Menino at his desk with the Stanley Cup. ... Boston scratched C David Krejci with an undisclosed injury. ... After being outshot 10-5 in the first period, Ottawa outshot Boston 10-9 in the second. ... Ottawa D Eric Gryba played in his 100th career game just down the road from where he played in college at Boston University. ... It was the third straight game in which a Boston player scored twice.