Rosehill dropped his gloves and challenged Paul Bissonnette, who obliged in what turned into a lengthy, two-round, blow-filled fight in front of the Philadelphia bench.
The Flyers were a different team the rest of the way, as Jakub Voracek scored the winner with 8:08 left and the Philadelphia finished with four unanswered goals in a 5-3 victory over the Phoenix Coyotes on Saturday night.
"I thought it was a great job from Rosie," Flyers coach Craig Berube said. "He's very smart at that. He picks the right spots and he's very good at his job."
Steve Mason made several difficult saves late to preserve Philadelphia's fourth win in five games out West.
"I thought this trip changed our road mentality a little bit," Berube said. "We discussed and talked about a lot of the little things we have to do on the road to win hockey games."
The little things are ailing the Coyotes, with Mike Smith struggling in goal again in a mistake-filled performance that left coach Dave Tippett lamenting "inconsistent" play and not ruling out roster changes.
"We're at the halfway mark and I'm sure (GM) Don (Maloney) and I will talk the next couple days," Tippett said. "We've got to evaluate where we are and where we want to get to."
Simmonds tied it with 15:38 left when he knocked in a rebound on the power play for his team-high 14th goal and his ninth in as many games.
Then Keith Yandle's turnover in his own zone proved costly in Phoenix's second straight loss. Voracek collected the puck and beat Smith between the legs with a wrist shot.
Philadelphia killed a late power play as Mason stopped 26 shots.
The Coyotes struggled defensively as they played without one of their top defenseman, Oliver Ekman-Larsson, who was injured Thursday on a hit by Columbus' Derek MacKenzie that earned him a three-game suspension.
Not even Doan's return from Rocky Mountain Fever could spark Phoenix.
Doan last played Dec. 4 before he started getting headaches, joint pain and severe fatigue. He was eventually diagnosed with the rare disorder that affects the lining of blood cells and is often contracted from bites by ticks.
Doan looked a step slow at times and his shifts were short. He logged 18:38 of ice time and his line failed to muster many scoring chances.
"He was all right," Tippett said. "He probably played a few more minutes that I had planned on."
After a scoreless first period in which the Coyotes went 0 for 3 on the power play, the teams combined for three goals in a 1:42 stretch early in the second.
Klinkhammer and Korpikoski scored just over a minute apart to make it 2-0 Phoenix amid shaky back line play by the Flyers.
Berube immediately called a timeout, and the Flyers responded 17 seconds later when Hartnell beat Smith on the glove side to extend his points streak to seven games.
But the Coyotes answered again at 6:47. Catching the Flyers on a line change, Yandle threaded a pass to Boedker at the blue line, and he skated in alone on a breakaway for his career-high 12th goal.
"These are games that in the past we would have played smart enough and our whole thing would have been sound enough where Philly felt like they played a really good game but didn't win," Tippett said. "We haven't had that feeling enough this year yet."
The comeback had begun.
"I think if someone told us before the road trip that we would get eight points we would take it right away," Voracek said. "It's a huge win for us."