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.
Susan Sarandon 'very excited' about daughter's pregnancy
Dennis Rodman pledges to end trips to North Korea