Sharp opened the scoring 2:34 into the contest and ran his season goal total to 21.
The Blackhawks, seeking their first division title in 17 seasons, boosted their lead over Nashville to 16 points in the Central.
Chicago won for the seventh time in nine games, getting 28 saves from Antti Niemi.
The Los Angeles goals came from Dustin Brown and Anze Kopitar less than 2 minutes apart in the second period. Los Angeles lost for the third time in four games despite 40 saves from Quick.
Notable deaths of 2014 [PHOTOS]