Adrian Kempe and Dustin Brown scored for the Kings, who were playing in their first road game of the season. Vince Dunn and Jaden Schwartz scored the other goals for St. Louis.
Jordan Binnington has started all five games for the Blues and is 3-1-1. He stopped 21 shots.
Kings backup goalie Calvin Petersen made his second start of the season and stopped 25 shots.
St. Louis recorded its first power-play goal of the season when the 29-year-old Krug scored at 13:12 of the first period. Krug, who signed a seven-year deal as a free agent last October after playing seven full seasons for Boston, scored on a one-timer from the point. Assisting on the goal were Perron and Ryan O'Reilly. It was O'Reilly's 100th assist as a member of the Blues.
''Those guys worked hard to recover pucks that whole shift, and I think we bobbled it a few times but they recovered it, made the right plays and Schwartz did the dirty work down in front of the net,'' Krug said. ''All the credit for the goal goes to those guys.''
Krug filled the void left by defenseman Alex Pietrangelo, who signed a seven-year, $61.6 million contract with the Vegas Golden Knights
St. Louis entered the game having not scored a power-play goal in its previous 14 chances this season. However, the Blues' power play had gone 5 for its last 6 against the Kings entering the game.
''Obviously our power play was not catching any breaks there,'' Krug said. ''We need to work a little bit harder and hopefully now that we've got one, the floodgates will open and we'll feel the confidence to continue to work.
Each team scored twice in the second period.
The Kings tied the game 1-1 just 57 seconds into the period. Kempe scored his third goal on a slap shot from the top of the left circle.
St. Louis came back with two goals to take a 3-1 lead. Dunn snapped in a wrist shot from the top of the slot at 2:53 for his first goal. Perron hit a wrist shot at 7:25 from the crease after getting a nifty no-look backhand pass from Robert Thomas, who also assisted on Dunn's goal.
''It was a nice play for sure,'' said Perron, who scored his first goal. ''Games pile up and you start thinking about it a little bit. This one went in so it was nice.''
Los Angeles enjoyed a two-man advantage and pulled within a goal at 3-2 when Brown pushed in the puck from the side of the net at 16:29 for a power-play goal.
But Los Angeles would get no closer.
''St. Louis is not a team you want to come from behind against,'' Los Angles coach Todd McClellan said. ''This team can lock it down. It's very comfortable playing with a lead. They give up very few chances and defend well.''
The Kings had five power-play opportunities.
''I don't want to talk about penalties,'' St. Louis coach Craig Berube. ''It causes a lot of problems. I liked the third period for the most part. We played a smart third period. I'd like to get that next goal. I think we are just a little tentative at times.''
Schwartz added an empty net goal at 19:58.
The Blues have won four straight against the Kings, outscoring them 16-5.
D Robert Bortuzzo (upper-body) remains out of action for St. Louis. The Blues did get back D Marco Scandella, who missed one game with an upper-body injury. For Los Angeles, LW Matt Luff (undisclosed injury) remains day to day. while RW Martin Frk (lower-body injury) and C Alex Turcotte (lower-body injury) remain week to week.
Heritage jerseys were back for the first of six Saturday night home games at Enterprise Center this season for the Blues. For the first time in franchise history, St. Louis will wear five different sweaters in the same season. Borrowing heavily from the team's inaugural uniforms from the 1967-68 season, this jersey made its return at the 2017 Bridgestone NHL Winter Classic. The vintage sweater look features the original Blue Note emblem on top of a light blue base with original gold and white stripes along the sleeves and waistline.
MASCOT STAYS SAFE
Blues mascot Louie, a blue polar bear who wears a Blues jersey with his name on the back, and the numbers ''00,'' wore a big black face mask as he did his routines during the game.
The Kings and Blues will conclude their two-game series Sunday night in St. Louis.
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