Jordan Kyrou had a goal and two assists for St. Louis, which surrendered at least four goals in each of its previous four games against the Kings. Pavel Buchnevich and Nick Leddy also scored, and Joel Hofer made 30 saves.
Buchnevich intercepted a pass from Phillip Danault and then set up Schenn, who beat David Rittich for his 13th goal.
“You just take off whenever you see a turnover in overtime,” said Schenn, a former first-round pick of the Kings. “Whether he gets you the puck or not, you just create space for him if he is going to carry it up. He’s got great vision and he found me.”
The Blues have won four straight games by a score of 4-3.
“We’ll take them since we’ve been on the right side,” defenseman Colton Parayko said. “It was a good game by our group. Maybe throughout the game, I thought we got better just from being on the road trip and coming back in the game. I thought we did a good job just building our game throughout as the game went on.”
Danault, Adrian Kempe and Jaret Anderson-Dolan scored for the Kings, who dropped their fourth consecutive game. Rittich made 28 stops.
The Kings are 2-8-6 in their last 16 games after a 20-7-4 start to the season.
“I think we played a pretty solid game,” Kings coach Todd McLellan said. “We got roasted on a bad line change. That can be cleaned up. You take that out and cut the penalties back, I think we had a good chance of winning, but we didn’t do that.”
Danault tied it 3-3 when he elevated a slap shot past Hofer for his 10th goal with 1:16 remaining in the second period.
Kyrou shot a feed from Scott Perunovich past Rittich for his 14th goal 12:07 into the second, giving the Blues a 3-2 lead. Robert Thomas picked up an assist on the play, giving him seven assists in his last five games.
“We’re finding a way to win, which is great,” Kyrou said. “It’s more of a mentality than anything. We’re playing really strong as a team. We always have each other’s backs out there. We’re playing together on the ice. That builds character, and we’ve shown a lot of resiliency these past couple games.”
Buchnevich tied it 2-2 with his 17th goal on a power play just 55 seconds after Anderson-Dolan scored his first goal of the season 5:39 into the second.
St. Louis went one for six on the power play.
“Way too many penalties,” Kings forward Trevor Moore said. “It starts with myself in the offensive zone, just stupid. We took a bunch of other ones so it gets guys out of the game. We played a pretty good game tonight, but it’s not enough and we can’t make mistakes like taking so many penalties.”
Leddy scored his third goal of the season 12:51 into the first, tying it at 1-1. St. Louis is 11-3-1 when a defenseman scores this season.
Kempe scored his 17th goal on a feed from Anze Kopitar 4:06 into the game.
Perunovich departed in the third because of a lower-body injury.