O'Reilly made a move around Wild forward Zach Parise and scored from between the circles.
Mackenzie MacEachern, Carl Gunnarsson and Sammy Blais scored, and Jake Allen made 20 saves for the Blues (9-3-3), who won in overtime for the second straight game and third time during the winning streak. St. Louis is 6-1-0 in its past seven games after going 0-2-2 in its previous four.
WATCH: [All Blues vs. Wild highlights]
"You have to find different ways to win, and that's what we're doing," Blues coach Craig Berube said. "I don't think we panic, we just stay with it. Things don't go our way all the time, that's the way it is and night in and night out, things don't go your way all the time, you just have to keep battling."
Marcus Foligno, Kevin Fiala and Mats Zuccarello scored, and Devan Dubnyk made 25 saves for the Wild (4-9-1), who have lost three games in a row and are 1-3-1 in their past five.
"I don't know what to say," Zuccarello said. "It's up to us in here, the group to win games. Bounces or not, that's going to go against you sometimes. You can't rely on that, you've got to earn it. … It's a boring answer, and you can say it as long as you want, but we were playing hard. We're all battling out there, trying to do our best. If we play like that, we're going to get some wins."
Foligno scored on a deflection at 2:26 of the first period for a 1-0 lead.
MacEachern scored 1:34 later to tie the game 1-1 at 4:00.
