Petr Cajanek and Jeff Woywitka also scored for the Blues (30-29-12).
Kyle Brodziak and Shawn Horcoff countered for Edmonton (30-35-7), which has been outscored 37-9 during their streak, which is one loss short of the club record. The Oilers also haven't won in nine games since dealing Ryan Smyth to the New York Islanders at the NHL trade deadline.
Cajanek opened the scoring with just 2:20 left to go in the first period, blasting a shot past Oilers goalie Dwayne Roloson for his 13th goal of the season.
Edmonton made it 1-1 just 40 seconds later when Brodziak picked up a loose puck in front of the Blues goal and beat goalie Curtis Sanford with a shot through his legs for first career NHL goal.
Woywitka's first career goal put the Blues back ahead 13 minutes into the second. Oiler rookie defenceman Brian Young's attempt to redirect a pass went right to a pinching Woywitka, who converted the miscue.
Edmonton tied it again halfway through the third as Horcoff scored the Oilers' first power-play goal in 32 attempts.
The Oilers play the third game of their six-game homestand Monday against Vancouver while the Blues are home to Ottawa on Tuesday.
NOTES: As badly banged up as the Oilers are with a staggering 11 players missing from their lineup, the Blues had seven players out for Saturday's game . . . The news only got worse for the Oilers in the second as one of their five remaining defencemen, Ladislav Smid, left clutching his side and did not return . . . Horcoff returned from a bout with the flu to replace Joffrey Lupul, the latest Oiler felled by the bug . . . Petr Nedved's second stint with the Oilers has ended. Nedved, knocked out of the lineup earlier this month with a knee injury, has left town in a move agreed upon by both himself and the team. The 35-year-old will be an unrestricted free agent this summer . . . St. Louis rookie David Backes has really picked it up offensively since early February. In the 14 games prior to Saturday's contest, he had eight goals and three assists. Prior to his hot streak, Backes had one career NHL goal in 22 games.