The Bruins fell three points behind the Tampa Bay Lightning for third in the Atlantic Division.
"[Losing leads] is something that kind of was happening at the beginning of the year," Boston defenseman Matt Grzelcyk said. "I thought we did a good job in the first, and then I don't know if it's fatigue or lack of urgency, but it's tough to see. … It's obviously something we've got to address."
Marc McLaughlin put the Bruins ahead 1-0 at 6:36 of the first when his redirection of Nick Foligno's centering pass deflected in off Senators defenseman Michael Del Zotto.
Froden, who was playing his sixth NHL game, made it 2-0 at 19:01 with a redirection in the slot off Grzelcyk's shot from the point.
"It was a good shot, and I lost my glove there on the play. I guess I had better feeling to tip the puck there. It was fun to get the first one," Froden said. "I was just trying to be in the lane and tip the puck there. I saw it went in. Amazing feeling."
Tkachuck scored 47 seconds into the second period to cut it to 2-1, banking the puck in off Swayman from below the goal line.
"We didn't like the way we played in the first period, and we wanted to come out back to our identity, and that was shooting pucks," Tkachuk said. "When we saw Swayman was in net, we just wanted to get as many shots as we could there. … That was a huge maturity moment for our team to come back, get back to our game, and not panic there."