Jonathan Quick notched 19 saves for the Kings, who trail the Blackhawks 2-1 in the best-of-seven series and will host Game 4 Thursday.
Justin Williams, Slava Voyonov and Dwight King scored for Los Angeles. The Kings outshot Chicago 28-20.
Quick faced only three shots in the second period but allowed a goal by Bryan Bickell on one of those shots that cut the Kings' lead to 2-1.
King made it 3-1 with an empty-net goal in the closing seconds of regulation.
Corey Crawford stopped 25 shots for the Blackhawks, who won the first two games of the series on their home ice.
Benedict Cumberbatch's dramatic reading of R. Kelly lyrics is just what you need
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'