Thomas got the puck at the inner edge of the left circle and whipped a wrist shot into the top shelf to help the Blues rally back from a 2-0 deficit.
Cam Fowler had a goal and an assist, Pius Suter scored, and Joel Hofer made 36 saves for the Blues (27-29-10), who were coming off a 3-1 win at the Carolina Hurricanes on Thursday and extended their point streak to seven games (6-0-1).
Connor McDavid and Kasperi Kapanen scored, and Connor Ingram made 22 saves for the Oilers (32-26-9), who lost 7-2 at the Dallas Stars on Thursday.
After a scoreless first period, the Oilers were pressuring heavily in the second period, and Kapanen finally put Edmonton ahead 1-0 at 15:41 when he took Leon Draisaitl’s backhand pass out of the corner to the slot and beat Hofer with a wrist shot. Draisaitl's assist on Kapanen's goal extended his point streak to eight games (five goals, 11 assists).
McDavid used his speed through the neutral zone to hem Blues defenseman Theo Lindstein in, whipping a wrister from the high slot past Hofer's glove to make it 2-0 at 9:56 of the third period.
Suter cut the deficit to 2-1 at 12:22 when he finished Jonatan Berggren's pass from behind the net to the low slot.
Fowler tied it at 16:14 with a wrist shot from the top of the right circle after Oskar Sundqvist won an offensive zone face-off.
St. Louis went nearly an entire period of play without a shot on goal. Forward Dylan Holloway had the last shot of the first period at 13:15 until forward Jordan Kyrou's shot on goal from the slot at 13:01 of the second period, going 19:46 without registering a shot.
The Oilers were playing without forward Ryan Nugent-Hopkins, who returned to Edmonton for personal reasons.
