Niemi picked up his first shutout of the season, the 14th of his career.
Demers scored on the power play with 2:52 left in the second period, assisted by Ryane Clowe.
The Sharks have won four straight, and are 12-2-1 since opening the season with three losses in four games.
Corey Crawford gave up one goal on 21 shots in the Blackhawks' third straight loss.
Members of Congress to keep receiving porn magazine
Justin Bieber crashes Drake Bell's album release party