The Philadelphia win, combined with the New Jersey Devils' 5-2 loss at the Chicago Blackhawks, moved the Flyers back into third place in the Metropolitan Division.
Mikael Granlund scored for the Wild and Niklas Backstrom made 27 saves as the Wild were swept in their back-to-back set. They lost 4-1 to the New York Rangers on Sunday. They've lost three in a row overall and are 1-7-1 in their past nine road games.
The Wild played without leading scorer Zach Parise, who was scratched due to a lower-body injury. Wild coach Mike Yeo said Parise would be evaluated further Tuesday.
Parise's absence didn't help a team that has 24 goals in its past 15 games and has scored one goal or fewer in eight of those 15 games.
"I'm not going to paint a rosy picture, and I'm not going to make any excuses," Yeo said. "Flat out, we need to be better. It's every one of us. It starts with me. We have to be better. ... There's no way we can accept this. It's not us. We have to fix it. That said, this is the same group that will fix it. I have no doubt. Am I worried? No. Ticked off that we're in this funk. But I also don't have any doubts that we'll fix it."
The Flyers appear to have fixed whatever ailed them. The win improved them to 13-6-3 in their past 22 games after their 4-10-1 start.
They'll take that confidence home for the Christmas break and hope it's there when they return to action with a six-game road trip that starts Saturday at the Edmonton Oilers and includes games at the Vancouver Canucks, Calgary Flames, Colorado Avalanche, Phoenix Coyotes and New Jersey Devils over an 11-day span.
"We got to take this show on the road," Flyers forward Scott Hartnell said. "You can't be homers and expect to make the [Stanley Cup] Playoffs and take the next step. We've got to take what we do at home and put it on the road."
Philadelphia led 2-1 after one period despite being outshot 11-5. Minnesota had a chance to tie the game with a two-minute power play to start the second after Simmonds was whistled for roughing at the final buzzer of the first period, but they failed to get a shot on net.
Instead, Philadelphia took advantage when Giroux skated through the slot to redirect a Braydon Coburn shot past Backstrom at 7:46 of the second for his 10th goal of the season to make it 3-1.
The Wild started the third period in a similar situation, with 1:32 of power-play time after a penalty on Voracek with 27.8 seconds left in the second. However, they again failed to capitalize on their chance and failed to get a shot on net.
"That's a critical moment," Yeo said. "I'm not going to sit here and say anything. ... The game wasn't good enough."
Philadelphia took its early lead by scoring on two of its first four shots.
Schenn opened the scoring 1:52 into the game with his third goal of the season. Hartnell took a pass in the Minnesota zone from Simmonds and carried the puck behind the Wild net. He tried moving out in front but lost the puck, which rolled into the right circle for Schenn, who one-timed the puck past Backstrom.
"It was a nice little play," Schenn said. "A chip by [Hartnell] right to me. I was just able to get a shot on net and get it through. I've been trying to get a couple of shots lately, and it's nice to see one finally go in."
The assist was the 500th point of Hartnell's NHL career. He's the 50th active player with at least 500 points.
Simmonds made it 2-0 with a power-play goal at 10:51 of the period. With Marco Scandella off for interference, Simmonds finished a tic-tac-toe passing play that saw Giroux throw a puck across the Minnesota zone to Voracek, who threw it back across to the far post to Simmonds for a tap-in goal.
"It was a great play from [Giroux] over to Jake, and Jake found me back door," Simmonds said. "I had a wide-open net, so it was pretty easy."
The assists extended Giroux's point-scoring streak to a career-best seven games and Voracek's to a career-best eight.
The Wild got on the board on Granlund's third goal of the season with 3:17 left in the first. Back-to-back penalties on Brayden Schenn and Coburn gave the Wild a two-man advantage for 1:40. They took advantage when Jason Pominville whipped a pass through the slot to Granlund, who beat Mason with a one-timer for his first goal since returning Sunday from an 11-game absence due to a concussion.
Giroux's goal in the second was his fifth in six games, and Simmonds added an empty-net goal with 57.0 seconds remaining in the third for the final margin.
The Flyers are winless in their past five road games (0-3-2) as they prepare to head off on the six-game trip after the Christmas break.
"Obviously, we've been hot at home," Simmonds said. "We just have to carry it on the road and play like we've been playing at home, and we'll be fine."
Yeo said he's looking forward to some time off as a way for his players to clear their heads and come back better when they return Friday for a game at the Winnipeg Jets, followed by four in a row at home.
"I think the break comes at the perfect time, no question," Yeo said. "I think it's pretty much all between the ears with us right now. ... We have to battle through it. We come back and we get to it."