Mason Lohrei scored for the Bruins (20-19-5), who lost their sixth straight (0-5-1). Jeremy Swayman made 27 saves.
"We're shooting ourselves in the foot time and time again," Boston forward Morgan Geekie said. "I feel like lots of these mistakes are kind of self-appointed ... but, yeah, we've got to figure it out in this room and we've got guys that can do that. I believe in each and every one of the guys in this room."
Anthony Cirelli gave Tampa Bay a 1-0 lead with a short-handed goal at 14:07 of the second period. McDonagh sent the puck down the ice to a streaking Hagel, whose shot from the slot went off the end boards before Cirelli scored on the rebound from the left face-off circle.
Over the past eight games, the Lightning are 17-for-17 on penalty kill with four short-handed goals.
"If we have a chance to go and create an opportunity for a goal or something, we're going to go," Cirelli said. "But in saying that, [the priority] first and foremost is to kill the penalty off and make sure we're not giving anything up."
The assist was McDonagh’s 400th point.
"It obviously feels good," McDonagh said. “Been playing with a lot of great teams over the years, a lot of great players. And it was funny, ‘Pointer’ said maybe a month and a half ago, ‘Oh yeah, you're [a few away from] 400. But I think I sat there two away for about a month, but it feels good."