Boston moved one point ahead of Tampa Bay for third place in the Atlantic Division and is three points behind the Toronto Maple Leafs for second.
"It's fun to play these sort of games when it's getting close to the playoffs and you're actually a part of it," Ullmark said. "There are still 11 games to focus on and we're not trying to get ahead of ourselves. We're trying to battle for home-ice advantage, and we've got to bring it every night."
Pierre-Edouard Bellemare scored, Corey Perry got his 450th NHL assist, and Andrei Vasilevskiy made 35 saves for the Lightning (43-20-8), who have lost four straight and seven of their past 11 (4-5-2).
"The process was really good tonight. Unfortunately, we fell behind again. We didn't like that," Tampa Bay coach Jon Cooper said. "But I didn't mind the way we were playing, and we answered right away. You need a push in the third period and I thought we gave it. ... The puck didn't go in for us and sometimes that happens.
"Did we want two [points]? We did. We got one. Let's take it and move on. Could we have easily gotten two tonight? We could've. Now we've got [the Buffalo Sabres on Sunday, a team] that has been playing well as of late. Let's continue taking steps forward."
Tampa Bay extended its lead on the Washington Capitals to eight points for the first wild card into the Stanley Cup Playoffs from the Eastern Conference.
"For us, we look ahead to the next game," Lightning defenseman Victor Hedman said. "We're not too worried about the standings or anything. It's about the process and this was a step in the right direction."
The Bruins took a 1-0 lead at 47 seconds of the second period after Lightning defenseman Erik Cernak turned over the puck in the defensive zone, allowing Brad Marchand to set up DeBrusk, who was alone for the backhand finish.
"I thought Jake was our best forward tonight in terms of all-around play," Bruins coach Bruce Cassidy said. "He was engaged in the game and trying to be physical on the forecheck. He was winning pucks and played a little on the (penalty) kill. He did a really good job for us."