It was the sixth loss in seven games for the Panthers. The Wild won their second straight after ending a four-game losing streak with a 3-2 win at Tampa Bay on Wednesday.
Niklas Backstrom stopped 32 shots for Minnesota, which leads the Northwest Division by two points. It was their sixth consecutive win by one goal.
"We will take it because it's enough to get two points," Wild coach Jacques Lemaire said.
"They [Minnesota] are a pretty good hockey team," Florida coach Jacques Martin said. "I thought in the third period we battled back hard. They were better than us the first two periods, that's for sure."
The Panthers cut the lead to 3-2 on Horton's power-play goal at 6:02 of the third. David Booth passed across the front of the crease to Horton, who poked in the puck from the left side.
Florida took 15 shots in the third period.
"I think we just ran out of time," Montador said. "Obviously, they're not a team you want to give a two-goal lead to. It was too little too late."
Minnesota took a 1-0 lead on Koivu's goal at 9:43 of the first. The Panthers turned the puck over in their own zone and the Wild had a three-on-one. Marian Gaborik passed from the right circle across to Koivu in the lower left circle. His wrist shot beat Vokoun.
The Panthers tied it 1-all on Montador's goal in the second. Montador beat defenseman Keith Carney to a loose puck in the left circle. His wrister went under Backstrom's pads at 5:34.
The Wild quickly reclaimed the lead. Veilleux grabbed the puck near the blue line and skated in on Vokoun. He faked a pass, then shot the puck over Vokoun's glove into the net at 7:54 to make the score 2-1.
Minnesota stretched its lead to 3-1 during a power play at 10:32 when Burns shot from the left circle beat Vokoun.
"We were really working it back and forth and just trying to move the puck quick, make tape to tape passes," Burns said. "On most power plays it's tough [for opponents] to keep going and going if we're making good passes."
The Wild play six of their next eight games at home.
"These games are important," Minnesota's James Sheppard said. "You can't afford to lose the first two then win the next two, not heading towards the playoffs. We can't have any more of this."
Florida is in danger of missing the playoffs for the eighth consecutive season and have lost 12 of 15 at home.
"Obviously, we're in a bad position," Vokoun said. "We have to focus on one game at a time. We need to win."
Newly acquired winger Chad Kilger might travel with the Panthers on Saturday for a two-game road trip. Kilger, who was traded to the Panthers from Toronto on Tuesday, is on a leave of absence for personal reasons. ... Florida's Bryan Allen (leg) was scratched and missed his second straight game. ... Minnesota's Gaborik picked up his first point in five games. ... Backstrom is 32-0-1 when going into the third period with the lead. ... Mark Parrish was scratched from Friday's game with the flu.