Matt Murray made 35 saves for Ottawa (16-24-4), which was shut out for the second straight game.
"It's obviously not the start we wanted," Senators defenseman Nick Holden said. "It's disappointing. We've been, for the most part, playing some pretty good hockey here. To come out like that [in the first period], and kind of put ourselves behind in the game, it's always hard to play catchup against teams like that."
Frederic gave the Bruins a 1-0 lead 45 seconds into the first period. Charlie Coyle made a move around Senators center Tim Stutzle along the right boards and passed to Craig Smith for a one-timer before Frederic scored on the rebound.
"We weren't ready. I mean, obviously on the first shift, they score," Ottawa coach D.J. Smith said. "That starts us on the wrong foot. You know, they're coming off a 6-0 loss (to the Carolina Hurricanes on Thursday), and they were hungry. We didn't match that in the first, I thought we did in the second, and then it's too late in the third."
Lazar made it 2-0 at 13:26 on a rebound at the top of the crease after Murray saved Anton Blidh's wrist shot off the rush.
Lazar, who played his first 176 NHL games with Ottawa, scored his first goal in eight games against the team that selected him No. 17 in the 2013 NHL Draft.
"Of course (there's a little extra boost)," Lazar said. "It's always fun coming back to this building. I have a lot of good memories here. It's where I got my start in the NHL. Obviously, to score against them is pretty cool too. … This one was special for myself. I want these wins really bad, and it was good to get those two points today."