The Flyers have lost eight of their last nine games at home (1-6-2) since opening the season 6-0 in Philadelphia.
After the game, the Flyers' players held a closed-door meeting for about 15 minutes.
"We talked about it as a team that we need to refocus and individually bring our best games to our team game every night," Flyers captain Jason Smith said. "We've got to play a lot better, compete a lot better, and capitalize a lot better. We can't be satisfied at working harder and losing games."
Hartnell put the Flyers ahead on a power play at 12:03 of the first period when he redirected a pass from R.J. Umberger past Ilya Bryzgalov, who had 26 saves.
"We didn't have any hits after period number one," Phoenix coach Wayne Gretzky said, "We didn't want to go out and think that we played a really good period. I was proud of how they responded afterwards."
Richards made it 2-0 when he poke-checked the puck away from defenseman Ed Jovanovski near the blue line and skated in to score unassisted at 7:21 of the second period.
The Coyotes scored twice in 2 minutes, 31 seconds, to pull even late in the second period.
After Yandle hammered in a rebound at 17:07, Sjostrom took a backhanded pass from Shane Doan and scored short-handed from the front of the left circle at 19:38.
It was the first goal of the season for Yandle, who was recalled from the minors on Dec. 10.
Biron made 39 saves for the Flyers, who were outshot 42-28.
"I thought as the game wore on, they [Phoenix] dictated the style of game that they wanted to play," Flyers coach John Stevens said. "We didn't allow ourselves to dictate the style of play that we wanted to play."
Smith played in his 900th NHL game. ... Phoenix D Matt Jones and Mike Zigomanis were healthy scratches. ... Philadelphia D Kimmo Timonen returned after missing two games with a lower-body injury. ... The Coyotes played the fifth of a six game road trip, their longest of the season. ... Philadelphia C Daniel Briere hit the post late in the second period. ... The Flyers had won four of their previous five home games against Phoenix.
Copyright by STATS LLC and The Associated Press
Arena: Wells Fargo Center Location: Philadelphia, Pennsylvania
Referees: Kerry Fraser, Chris Lee Linesmen: Brian Murphy, Jonny Murray
Attendance: 19,211 (98.5% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Scott Hartnell (5)
(Power Play) Assist: R.J. Umberger
Mike Richards (16)
Keith Yandle (1)
Assists: Niko Kapanen, Mathias Tjarnqvist
Fredrik Sjostrom (9)
(Shorthanded) Assist: Shane Doan
Peter Mueller (9)
Assists: Zbynek Michalek, Steve Reinprecht