Midway through the second period, Sawada lost control of the puck in the Bruins' zone and, as he reached to retrieve the puck, Paille made contact with his head and shoulder, sending the Stars' forward sprawling.
Paille was assessed a match penalty for illegal hit to the head and a 10-minute misconduct on the play.
"Paille delivered a lateral hit where the principal point of contact was his opponent's head," said Senior Vice President of Hockey Operations Mike Murphy. "Additionally, the injury suffered by the Dallas player was a factor in this decision."
Sawada suffered injuries to his nose and shoulder as a result of the hit.
Murphy handled the hearing in place of NHL disciplinarian Colin Campbell, whose son Gregory plays for the Bruins and was involved in Thursday's game.
"It was a bad hit," said Bruins defenceman Andrew Ference after the game. "We can't be hypocrites when your own team does a hit like that which the league is trying to get rid of."
But Bruins head coach Claude Julien didn't share Ference's opinion on the hit, pointing out that it was Sawada who was playing with his head down.
"Once you're in the pros, you've been told for many, many years never to play with your head down," Julien said. "So if he hasn't learned by now, he shouldn't be in the pros."
The game got off to a nasty start with three fights in the first four seconds. When it was all said and done, both teams combined for 89 minutes in penalties.
Paille is eligible to return Feb. 15 against the Toronto Maple Leafs.