James Neal scored with 1:50 remaining with a sixth attacker on to cut it to 2-1. He was able to curl around the net and collect a loose puck and whip it into an empty net from a sharp angle.
"We had some good opportunities but we didn't find the net until late," Oilers defenseman Adam Larsson said. "It's kind of the story of the game."
The Blues challenged for goaltender interference, claiming Zack Kassian interfered with Allen, but the call was confirmed on video review.
"We gave it a try," Allen said. "I think it was a 2-0 game, and honestly, 6-on-4 is a lot easier than 6-on-5. I sort of like the 6-on-4 better. You don't have to worry about the icings, it gives the other team more time and space to think. When you think you usually take plays a little bit for granted and it's easier for us because we can just stay in our structure, our PK structure. On the 6-on-5, you get a little running around."