Logan Mailloux put St. Louis up 4-3 at 17:03 with a backhander from the edge of the right face-off circle past Karel Vejmelka's glove.
Thomas then completed his second hat trick in the NHL with an empty-net goal at 19:22. He scored his first hat trick back on April 5.
Pavel Buchnevich scored to extend his goal streak to three games, and Dylan Holloway had two assists for the Blues (37-33-12), who finished their season on a four-game winning streak. Joel Hofer made 20 saves.
Lawson Crouse, Michael Carcone, and Kailer Yamamoto scored for the Mammoth (43-33-6), who have lost three of four to end their regular season. Clayton Keller and MacKenzie Weegar each had two assists.
Vejmelka allowed three goals on 18 shots before he was replaced by Vitek Vanecek to begin the third period. Vanecek made nine saves in relief.
Utah will begin its Western Conference First Round series against the Vegas Golden Knights on Sunday.
Buchnevich gave the Blues a 1-0 lead at 3:45 of the first period. Jordan Kyrou deflected the puck between his legs from behind the net to Buchnevich, who lifted it over Vejmelka's pad at the right post.
Carcone tied it 1-1 at 16:55, taking a touch pass from JJ Peterka and burying a wrist shot from between the circles to the blocker side.
Crouse put Utah ahead 2-1 just 45 seconds into the second period. Weegar's shot from the point hit traffic in front, and Crouse backhanded the loose puck into an open net.
The Mammoth appeared to make it 3-1 at 1:26, but St. Louis challenged the play for goaltender interference on Brandon Tanev and the goal was overturned after video review.
Thomas evened the score 2-2 at 8:14. Holloway backhanded the puck into the slot from the right of the net, and Thomas sent a snap shot past the outstretched glove of Vejmelka.
Thomas scored his second of the period to put the Blues up 3-2 at 11:07, redirecting Cam Fowler's pass from the blue line to the blocker side from in front.
Yamamoto tied the game 3-3 at 18:52 when he put a wrist shot past Hofer's glove from the slot.
The Mammoth were without forward Dylan Guenther (undisclosed) and defenseman Sean Durzi (upper body), who was injured in a 5-3 win against the Winnipeg Jets on Tuesday.
