Bruins coach Claude Julien brushed off a question about whether the loss hurt more because Seguin and Peverley played such big roles.
"I don't care about that. Give it a break," he said. "I'm mad because we lost."
Seguin scored on Dallas' second shot, tying the shootout 1-all after Patrice Bergeron scored on Boston's first attempt.
Then Peverley put the puck through Tuukka Rask's pads on the Stars' fourth and final shot.
"I think I was more nervous for this game than I was for any of the Stanley Cup finals," Peverley said. "It was emotional for me, but it was fun to be here."
The Bruins lost those finals in six games to the Chicago Blackhawks. Now they have lost four of five games after winning four in a row.
"The first 10 minutes were good, and then we got back to some of our old habits," Julien said. "Eventually, when you play that way, you find ways to lose hockey games, and that's what we're doing right now."
It was the second straight shootout win for the Stars. On Sunday, Jamie Benn scored the winner in a 4-3 victory over Ottawa.
The other goals came in the first period with Benn scoring for Dallas at 3:38 and Torey Krug tying it at 4:16.
Seguin, the second pick in the 2010 draft, and Peverley were sent to Dallas after last season in a trade that brought forwards Loui Eriksson and Reilly Smith to Boston.
Seguin, who leads the Stars in scoring, was booed several times when he touched the puck and was taunted with the chant, "Say-gin, Say-gin."
"I am sure that there are mixed feelings out there," he said. "I can only go out there and play hockey."
It was the first meeting between the teams since Dec. 31, 2011, when Dallas won 4-2. The clubs hadn't faced off in Boston since Feb. 3, 2011 -- a 6-3 Bruins victory.
On the penalty shot that forced overtime, Fiddler skated up the left side, cut across the crease and lifted a backhander into the upper right corner of the net past Rask.
Lucic's seventh goal matched his total for last season. Stationed in front of the net, with teammate Jarome Iginla and two Stars, Lucic redirected Hamilton's shot past goalie Kari Lehtonen.
Eriksson returned after sitting out five games due to a concussion. He missed his shootout attempt on Lehtonen.
"I've been shooting a lot of pucks on him, and he's a great goalie," Eriksson said. "He's a big goalie, takes up a lot of the net, so you have to find a good shot against him or make a good move, and I didn't, so it was bad."
Alex Chiasson missed the next shot for Dallas, and David Krejci failed for Boston. Then Peverley, who was booed when his name was announced as the final shooter, came through.
"I knew it was going to be a big night for (Seguin) and Rich both. Sometimes you don't know exactly how they're going to react to it," Dallas coach Lindy Ruff said. "Both Rich and him scoring in the shootout, I think it was great for both of those players."
Red Sox first baseman Mike Napoli watched the game from a luxury box. He tugged on his long beard when shown on the video screen. ... Benn has nine points in nine road games. ... The Bruins allowed the first goal for the fourth straight game and sustained their third loss in that span.
Copyright by STATS LLC and The Associated Press
BOSTON, MA - NOVEMBER 5: Tyler Seguin #91 of the Dallas Stars skates during warm ups prior to the game against the...