Raymond tied it 2-2 at 14:09, taking a pass from Nick Leddy and scoring into the empty side of the net. Vrana made it 3-2 with a power-play goal at 18:31, lunging for a one-timer off Filip Hronek's pass.
"In the past few games, we've really sunk when the other team has scored first, and it was a point of emphasis tonight to stay with our game when things got tough," Red Wings captain Dylan Larkin said. "Tonight, they scored first and we responded with a really good period and ended up with the lead."
Raymond put Detroit up 4-2 at 5:52 of the second period when he knocked in Leddy's pass from the top of the crease.
Zuccarello made it 4-3 with a power-play goal at 9:31, and Jordan Greenway had a tying goal disallowed after a Red Wings challenge. The officials ruled Eriksson Ek pushed Pius Suter into Nedeljkovic.
Greenway has gone 21 games without a goal since scoring twice in a 5-2 win against the San Jose Sharks on Dec. 9.
"[Eriksson Ek] owes me one," Greenway said.
Boldy tied it 4-4 at 3:04 of the third period, and Kaprizov gave Minnesota a 5-4 lead at 13:13.
NOTES: Red Wings forward Robby Fabbri left the game in the second period with a lower-body injury. Blashill said he didn't know the severity of the injury. … Boldy scored his first NHL hat trick against the Red Wings on Feb. 14. … The win was Minnesota's NHL-leading seventh this season after trailing by multiple goals, the most in its history. The Wild are tied for the NHL lead with 17 one-goal victories. … Detroit has allowed 41 goals in its past seven games, including 20 in the past three. … Kaprizov has scored 10 points (six goals, four assists) during a seven-game point streak.