Corey Crawford made 21 saves, and the Blackhawks generated just enough offense to improve to 7-1 at home in the playoffs.
Game 2 is scheduled for Sunday.
Williams has scored the last three goals for the defending Stanley Cup champion Kings. He was responsible for all of Los Angeles' offense in a 2-1 victory over the San Jose Sharks in Game 7 of the second-round series on Tuesday.
The Blackhawks and Kings returned to the ice after getting through strenuous second-round series.
Top-seeded Chicago stormed back to beat Detroit after trailing 3-1 in the series, winning Game 7 on Brent Seabrook's overtime goal Wednesday night. Fifth-seeded Los Angeles was pushed to the brink of elimination by the Sharks in a series in which the home team won every game.
For the first period and much of the second of the conference finals opener, Chicago looked hopeless against Quick and Los Angeles' talented defensemen.
As they did against Detroit, the Blackhawks began to create more quality chances when they put more traffic in front.
With 7 1/2 minutes left in the second, Sharp skated into the zone, left the puck for Johnny Oduya and kept moving forward. When Quick kicked away Oduya's slap shot, the puck went right to Sharp, who scored into the lower right corner to tie it 1-1 with his eighth playoff goal.
Sharp created another strong opportunity a few minutes later, but Brandon Saad shot wide right on a potential tip-in.
The Blackhawks kept up the pressure and went ahead when Hossa had a beautiful midair tip on Duncan Keith's long slap shot at 16:22 of the second. The puck landed in the lower right corner again before Quick could find the puck in the group of bodies near the net.
It was the sixth goal of this postseason for Hossa and the 42nd of his playoff career. The 34-year-old forward has at least one point in four straight games.
Los Angeles turned up the pressure at the beginning of the third, but Chicago killed off a power play. Crawford was solid after an early gaffe played a role in the Kings' goal. He stopped Dustin Penner's tip attempt with a little more than five minutes left, preserving Chicago's lead.
Crawford has allowed just one goal in four of five games, playing a huge role as Chicago rallied to eliminate Detroit.
Chicago controlled most of the first period, using its speed and skill to keep the puck away from Los Angeles. The Blackhawks had nine shots on goal before Crawford was tested for the first time, grabbing Penner's attempt with 8:11 remaining.
While Quick turned away every charge at the other side, Los Angeles made the most of its second shot after a couple of costly Blackhawks misplays.
After the puck was dumped into the Blackhawks' zone, Crawford went behind the net to try to clear it away, but Brad Richardson jumped in the air and knocked it in front. Dave Bolland then tried to break up the play, but the puck went right to Williams, who beat Crawford to make it 1-0 at 14:23.
Most of Chicago's shots in the first period came from the outside, and Quick had a clear lane for most stops. The 2012 Conn Smythe Trophy winner as playoff MVP made 17 saves in the first 20 minutes.
Crawford faced only two shots in the first period and stopped one.
NOTES: Kings C Jarret Stoll returned to the lineup. He has been sidelined with a suspected concussion since he was struck with an illegal hit to the head by San Jose's Raffi Torres in Game 1 of Los Angeles' second-round series against the Sharks. ... This is the second playoff series between the Kings and the Blackhawks. Chicago advanced in five games in the 1974 quarterfinals. ... There was no shoot the puck competition after the second period, part of an NHL mandate designed to preserve ideal ice conditions.