Moore took the puck from his own zone and skated down the right side before getting behind Jonatan Berggren for a wrist shot from the bottom of the right circle.
Robert Thomas tied it 1-1 with 3:53 remaining in the third period for St. Louis when Philip Broberg’s long shot took multiple deflections before going in off Thomas’ skate.
Adrian Kempe scored a power-play goal, and Anton Forsberg made 23 saves for the Kings (30-26-18), who had lost six of their previous eight (2-3-3).
Los Angeles moved into the second wild card into the Stanley Cup Playoffs from the Western Conference, one point ahead of the San Jose Sharks and Nashville Predators, who the Kings will host on Thursday.
Jordan Binnington made 24 saves for the Blues (31-31-12), who had points in four of their past five (4-1-1), but have lost two straight.
St. Louis is four points behind the Kings for the second wild card.
Kempe’s power-play goal put Los Angeles ahead 1-0 at 16:59 of the second period. He took Alex Laferriere’s backhand pass through the slot and scored on a wrist shot from the right circle for his 28th goal of the season.
Artemi Panarin had the secondary assist, his 19th point (seven goals, 12 assists) in 18 games since being acquired from the New York Rangers on Feb. 4.
Jared Wright appeared to score for Los Angeles 8:28 into the second, but his goal was immediately waved off for goaltender interference by Joel Armia.