Chicago (14-0-3) broke the record set by the 2006-07 Anaheim Ducks, who earned points in their first 16 games.
In Friday's other games, Vancouver broke a scoreless tie in the third period to beat Nashville and Pittsburgh downed Florida.
Chicago rookie Brandon Saad scored a short-handed goal early in the third period to snap a 1-1 tie as the Blackhawks notched their fourth straight win.
Viktor Stalberg also scored for league-leading Chicago, which has captured a total of 31 of 34 possible points.
Patrick Marleau scored for the Sharks, getting only his second goal in 11 games after getting nine in San Jose's first five games.
Vancouver's Dale Weise scored the sole goal at 9:14 of the third period and the Canucks held on for a 1-0 win at the Nashville Predators.
Goalie Roberto Luongo made 23 saves for the shutout.
Chris Kunitz also scored for the Penguins, who lost star center Evgeni Malkin in the third period after he took an off-balance check and slid back-first into the end boards. Malkin remained down on the ice for several moments, but skated off the ice on his own.
Florida defenseman Mike Weaver scored the Panthers' goal.