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.
Notable deaths of 2014 [PHOTOS]