Matt Walker was sent off for hooking with 1:30 to go in the extra session, but it appeared the game would go into a shootout before Jarret Stoll unleashed a slap shot from the point. Hannu Toivonen made the stop, but Penner kicked the rebound to his stick and slid the puck past the goaltender.
Edmonton halted a six-game losing streak by handing the Blues their ninth setback in 12 games. The Oilers have not won in regulation since a 4-0 victory over Anaheim Dec. 2.
Mathieu Garon got the victory with 31 saves.
St. Louis goaltender Manny Legace left the game in the first period with a head injury.