Stephen Johns and Alexander Radulov scored for the Stars (25-17-3), who started their four-game road trip by winning for the third time in four games. It was Dallas' first road win in its past four games (1-2-1).
Kari Lehtonen, starting in place of Ben Bishop, made 30 saves in his first start since Dec. 15.
"He was sound," Dallas coach Ken Hitchcock said. "That's what you hope for. He's a backup in word only; he's really a starting goaltender. We've got the luxury and we've got to start using it right now."
Zdeno Chara and Ryan Spooner scored, and Khudobin made 29 saves for the Bruins, who had won their past five home games. Boston trailed 2-0 in the second period and were behind 2-1 to start the third period before rallying to earn a point.
"That's the positive in this game. We were down two and we were able to scratch back against a very good defensive team," Bruins coach Bruce Cassidy said. "It's one thing to do it against a team that gives up a lot, but this is a good defensive team. So that's the positive in it all."