Crawford stopped all 13 shots he faced in the first period.
Andrew Shaw and Brent Seabrook each scored for a quick 2-0 Chicago advantage. The Blackhawks chased Kings goalie Jonathan Quick early in the second period when Bryan Bickell made it 3-0 on a power-play tally and Michal Handzus quickly followed with another goal.
Brandon Saad and Patrick Sharp each supplied two assists as the top-seeded Blackhawks won a second game in two nights over the fifth-seeded Kings and notched their fifth straight post-season victory.
Tyler Toffoli provided a goal and an assist and Jeff Carter also scored for Los Angeles.
Quick let in four goals on 13 shots before being lifting the second period.
Jonathan Bernier finished up with nine saves.
The Kings will attempt to get back into the series when they host Tuesday's Game 3.