Brandon Saad added a goal and an assist for defending Stanley Cup champion Chicago, which remained perfect in seven home playoff games this year. Duncan Keith had a tiebreaking score in the third period.
Playing just two days after a Game 7 victory over Anaheim, the Kings got a second-period score from Tyler Toffoli and outshot the Blackhawks 26-20 in the opener of a rematch from last year's Western Conference final. But Crawford made a couple of solid stops in another terrific performance.
Game 2 of the best-of-seven series is Wednesday night.
Quick made 17 saves after he played a key role in Los Angeles' rally from a 3-2 deficit in the series against the Ducks. The Kings also battled back from a 3-0 deficit against San Jose in the first round.
Toews' 26th career playoff goal came after he had one waved off in a confusing stretch in the second period.
It looked as if Chicago had a 2-0 lead when Toews' rush to the net resulted in the puck going off the skate of Kings defenseman Slava Voynov and into the goal. But it was waved off after a conference by the officials, prompting a round of boos from the crowd of 21,832 and a waving, yelling display from Blackhawks coach Joel Quenneville.
According to the NHL, the original call of good goal was changed because the officials decided Toews made incidental contact with Quick before the puck crossed the goal line. The league said the ruling was not reviewable, so the call on the ice remained in place.
The sequence seemed to wake up the Kings while deflating the Blackhawks. Los Angeles got its first goal about a minute later, with Tanner Pearson making a terrific pass to the middle to Toffoli for his fourth of the playoffs at 4:35.
The Kings then had a couple of chances to take the lead, but Crawford stepped up each time. He denied Kyle Clifford on a 2-on-1 break with 13:42 remaining, and stopped Marian Gaborik and Dustin Brown in rapid succession midway through the period.
Crawford's solid play bought Chicago some time to shake off the disallowed goal, and it paid off when Keith's slap shot went off the stick of Kings forward Trevor Lewis and bounced past Quick for a 2-1 lead at 11:54.
Crawford made another big save on Jeff Carter in the first minute of the third, and Toffoli had a backhander go off the outside of right post on a breakaway opportunity in the final period.
The Blackhawks used a bad penalty by Kings defenseman Alec Martinez to grab the lead in the first period. Martinez pushed forward Brandon Bollig to the ice long after the whistle had blown, drawing a roughing call.
Saad redirected Nick Leddy's slap shot past Quick in the final seconds of the resulting power play. Saad's third goal of the playoffs made it 1-0 with 5:14 left in the period.
The Kings had a prime scoring chance with 2:42 to go in the first, but Leddy tied up Mike Richards at the end of a 2-on-1 break. It was part of a nice all-around performance for Leddy after he was a healthy scratch for Game 3 of Chicago's second-round series against Minnesota.
NOTES: Kings D Willie Mitchell was active for the first time since Game 6 of Los Angeles' first-round series against San Jose, but D Robyn Regehr remained out with an injury. He has missed the Kings' last seven games. ... Blackhawks D Michal Rozsival was active after he was a healthy scratch for the last two games of their second-round series against Minnesota.