Edmonton mustered 30 shots on goal, went 1-for-3 on the man-advantage, dished 32 hits and won 53 percent of their faceoffs.
In goal, Cam Talbot allowed four goals against on 39 shots but his club was ultimately outplayed in the final 40 minutes of the game.
"They threw 19 shots at us in the second period and I thought we fed their transition an awful lot," said Oilers Head Coach Todd McLellan. "We'd get the puck over the blueline, we'd pull up, turn it over and they'd be coming back the other way.
"They were better than us in a lot of areas tonight and they got the win."
The first period between the Oilers and Blues saw it all: goals - power-play and shorthanded - a fight, scrums and big saves.
Zack Kassian and Chris Thorburn dropped the gloves no more than three minutes after the opening faceoff. The animosity began there, as scrums ensued several times after the whistle throughout the period.
A pair of goals came while former Oilers forward Magnus Paajarvi was in the box for holding. St. Louis disrupted Edmonton's power-play setup, icing the puck down to Talbot. The Oilers netminder went to play the puck behind the net but bobbled it, gifting Vladimir Sobotka a gimmie at 15:14.
But the Oilers made good on the power-play time remaining 29 seconds after Sobotka's strike.
Ryan Strome corked a wrist shot from the right circle that beat Blues goalie Jake Allen clean, tying the game up at 1-1 with his third of the campaign. Matt Benning and Ryan Nugent-Hopkins got the assists.
Talbot, meanwhile, bounced right back after the mishap. He extended his left pad on Paajarvi to keep the puck out, then slid across to the right side of the net when the winger tried to wrap it around, making two of his 12 first-period saves.
Despite Talbot's best efforts to keep the game squared up at one in the second period, St. Louis gained the lead with a Steen power-play marker. The Blues forward got two whacks at the puck inside the blue paint, the second of which Talbot couldn't stop because he had fallen onto his back.
Talbot didn't let up, stopping 18 of the 19 shots he saw in the middle frame, one of which came on a threatening Vladimir Tarasenko wrister while on a 2-on-1 but the Blues poured it on in the third.
"They had a tenacity of back-checking, shutting lanes down, having good gaps and we wanted to play East-West at the blueline," said McLellan.
Schenn made it 3-1 at 5:44 of the final period with a snipe from the left side on another 2-on-1 given up by the Oil.
"We weren't good enough defensively," said defenceman Benning.
Schenn added a second insurance goal with his second of the period less than three minutes later. He popped home a nifty pass from Jaden Schwartz that Talbot had no chance on, giving St. Louis the run support they would need to close the game out.
Colton Parayko got his knee mixed up with Milan Lucic in the period. Lucic let Parayko know of his frustration, as he tried to engage the defender physically but Parayko had none of it and Lucic was given a penalty. He hobbled off to the dressing room with a misconduct and Patrick Maroon served his roughing penalty.
The two clubs will meet again five days from now in St. Louis.
"They capitalized on some opportunities that we fed them," said McLellan. "It wasn't our best. If we throw our best at them, I think we come away with a chance to beat them."