Darroll Powe supplied the lone goal for Minnesota, which has gone 2-10-4 over its last 16 games.
Josh Harding surrendered five goals on 34 shots in the loss, the 10th in row on the road for the Wild.
Wild forward Matt Cullen took Philadelphia's Claude Giroux down in the offensive zone, and Timonen scored on the subsequent power play, firing a slap shot from the point through heavy traffic at the 2:56 mark of the first period.
Giroux picked up the primary assist for his 200th career point.
The Flyers and Wild combined to score three goals in a 2:20 span during the second period.
First, Couturier partially fanned on a return feed from fellow standout rookie Matt Read but it still trickled into an open net for a short-handed goal at 10:27. The 2011 first-round pick extended his goal-scoring streak to five consecutive games.
Powe, a former Flyer, quickly answered with his first tally since December 8 at 11:38, but Coburn replied for Philadelphia at 12:47.
The Flyers' power-play unit then struck again as Hartnell notched his 20th goal of the season on a redirection, extending the lead to 3-1 at 16:04 of the middle stanza.
Voracek added a goal in the third period.
Hartnell notched 20 goals for the sixth time in his career...The Flyers improved to 8-2-2 against the Western Conference this season...Minnesota's Devin Setoguchi played in his 300th career game...Powe played with Philadelphia for three seasons (2008-11).