In the second straight dramatic contest between the Blues and Kings, St. Louis turned a third-period deficit into a victory.
The Kings will host the third and fourth games of the Western Conference quarterfinal series on Saturday and Monday.
St. Louis won the first game against the Kings in overtime and this contest appeared headed toward an extra session as well.
Los Angeles came up with its only goal midway through the first period on a power-play score from Dustin Brown.
Brian Elliott made 28 saves to claim the victory, his second in these playoffs. Quick stopped 23-of-25 shots.