Luke Schenn and Claude Giroux also scored for the Flyers, whose record rose above .500 for just the second time this season (17-16-4).
Mikael Grandlund tallied for the Wild, who fell to 2-7-0 all-time at the Wells Fargo Center. The Wild are 1-7-1 in their last nine road games.
Both teams are off until Friday.
Schenn opened up the Flyers' scoring on the team's first shot of the game, less than two minutes after the opening faceoff. Charging through the circle, he sent a trickling pass from Scott Hartnell past Wild goalie Niklas Backstrom to give the Flyers a lead they never lost.
Simmonds added to it about eight minutes later, thanks to some pretty tic-tac-toe passing on the power play.
The Flyers, who struggled in their last outing in Columbus Saturday, welcomed a tired Wild team, who played just a day earlier in New York. Minnesota traveled to Philadelphia after falling to the Rangers 4-1 Sunday. Backstrom started both games.
"Obviously we didn't have a good game last game," Schenn said. "This being our last home game for a while, we wanted to get off to a good start, be physical and tough to play against in our own building."
The Wild cut the Flyers' lead in half late in the first period, capitalizing on a 1:40 two-man advantage. A very patient Grandlund had been left alone by the Flyers' defense, and beat goalie Steve Mason with backdoor shot.
Mason, though, was strong for the Flyers for the entire 60 minutes Monday, stopping 26 of the 27 shots he faced.
In the second period, the Flyers hit the ice with noticeably improved energy. Giroux scored the lone goal of the period, redirecting a shot from the point by Braydon Coburn.
Simmonds added an empty-netter in the closing seconds of the final period to bring the score to 4-1.
NOTES: Hartnell's assist on Schenn's first-period goal was the 500th point of his career. . Zach Parise missed the game with a lower-body injury. . Giroux extended his point streak to seven games, a career high.