Minnesota outshot St. Louis 16-7 in the second period, but Hoffman started the Blues rally in the third when he one-timed a pass from David Perron on the power-play at 3:49 to cut it to 3-2.
Jordan Kyrou tied it 3-3 at 7:41 after a turnover by Matt Dumba.
"I thought the third period, we came out with a different mindset than we did in the second period," Blues coach Craig Berube said. "I was happy [with the] first and third period tonight; second period, obviously not so happy."
Brodin gave the Wild a 1-0 lead at 17:47 of the first period with a slap shot from the top of the left circle. Joel Eriksson Ek scored on a rebound 32 seconds into the second period to make it 2-0.
Hoffman took a pass from Vladimir Tarasenko for a power-play goal to cut it to 2-1 at 10:27. Foligno scored 1:02 later with a snap shot from the right circle to make it 3-1 at 11:29.
"They're a desperate team right now and they're going to play to win there at the end," Talbot said. "When it comes down to it, that's when you need a save, especially with 23 seconds left. [I've] just got to get a blocker on it, got to get something behind that one.
"It's just a tough one to swallow when you're so close to at least getting a point, taking it to overtime and anything can happen there. Third period, we needed a save and didn't get one tonight."
NOTES:Wild forward Kirill Kaprizov had his five-game goal streak end. … The Blues have scored a power-play goal in eight straight games. … St. Louis defenseman Colton Parayko missed his second straight game because of an upper-body injury. Berube said it's possible Parayko could play Thursday. … It was Kyrou's first goal in 15 games since he scored twice at San Jose on March 20. … Hoffman has scored 11 points (seven goals, four assists) in the past seven games. … It was Talbot's first regulation loss in eight games.