Pavel Buchnevich cut it to 4-3 at 8:37 with a wrist shot from between the face-off circles.
Dvorsky gave the Blues a 1-0 lead at 2:29 on their only shot of the first period, beating Gibson from the slot off a rush after a feed from Barron.
J.T. Compher tied it 1-1 at 8:13 on a tap-in after Michael Rasmussen stole the puck from Hofer behind the net.
Detroit outshot St. Louis 8-1 in the first.
“They defend really well and they make it hard to forecheck,” Blues coach Jim Montgomery said. “I didn’t think we had our checking legs for the first 30 minutes and we weren’t putting pucks in the right spots.”
Keegan Kolesar gave the Red Wings a 2-1 lead just 41 seconds into the second on a breakaway. It was his first point in 14 games this season.
Raymond made it 3-1 with an unassisted goal at 13:14. He had the puck in the left corner, circled out to the high slot and put a wrist shot past Hofer’s blocker.
Snuggerud cut it to 3-2 on a rebound at 19:32. Robert Thomas won a puck battle along the boards and cut to the net and Gibson made the initial save, but Snuggerud was there to tuck it home.
“I thought we started having some turnovers in the second period, but if we get through the period, we can fix things,” McLellan said. “But we make a sloppy play and get scored on, and all of a sudden the momentum is going their way.”
Emmitt Finnie restored the Red Wings’ two-goal lead with a power-play goal at 3:29 of the third, scoring from the slot to make it 4-2.
NOTES: Kaskimaki is the second Blues player in the past 10 years whose first NHL goal stood as the game winner (Jake Neighbours on Oct. 23, 2021). … Thomas had one assist, was plus-2 and won 14 of 21 face-offs (66.7 percent). … Blues defenseman Philip Broberg had three blocked shots and led all skaters in ice time (27:09). … Red Wings forward Michael Brandsegg-Nygard had six hits in 15:40