Schneider helped the Devils end a three-game losing streak while handing the Stars their fourth straight loss.
Dallas gave up 18 goals in its previous three games, but New Jersey managed only a lone score from Michael Ryder midway through the second period.
Schneider made that goal stand up, however, while picking up the 12th shutout in his six NHL seasons. He spent the first five years of his career with Vancouver.
Kari Lehtonen stopped 33-of-34 shots for Dallas.