Carter pulled the Flyers into a 3-3 tie with 1:07 left in regulation when he deflected Richards' slap shot past Tellqvist.
"I'm more disappointed in the [missed] power play in overtime than I am in their score late in the game," Phoenix coach Wayne Gretzky said.
Carter's goal came after Fedoruk put the Coyotes ahead 3-2 at 14:46 of the third period when his wrist shot bounced in off Philadelphia defenseman Lasse Kukkonen.
Richards had nothing but praise for Carter, who went into the game second in the NHL with 13 goals.
"He is really playing unreal," Richards said. "He's doing a lot of good things on the penalty kill and on the power play. Right now he's doing everything he can to win us hockey games."
Knuble tied it at 2 with a power-play goal at 5:08 of the third. Standing with his back to the net, Knuble deflected Kimmo Timonen's shot past Tellqvist's glove side.
"We played a pretty solid game and let it slip away," Coyotes defenseman Ed Jovanovski said. "With Murphy's law, it just broke down and went the other way."
Phoenix went ahead with 51 seconds left in the second period on a fluke goal that was credited to Hanzal.
Zbynek Michalek's slap shot from just inside the blue line was knocked down by Luca Sbisa, but the Flyers defenseman got tangled up with Hanzal while falling down and his stick inadvertently swept the puck between Biron's pads.
Hartnell put the Flyers ahead at 6:18 of the first period with an unassisted goal. His shot from the left circle bounced off the skate of Michalek into the net.
Carcillo tied it for the Coyotes on a power play with 1:10 left in the period. It was his first goal in 15 games, dating to April.
Hanzal prevented Biron from clearing the puck cleanly from behind the goal, and Carcillo skated in and swept it into the open net.
Phoenix C Peter Mueller played in his 100th NHL game. ... Philadelphia C Simon Gagne extended his point streak (3 goals, 7 assists) to seven games with an assist on Knuble's goal. ... Phoenix RW Brian McGrattan and C Garth Murray were healthy scratches. D Derek Morris sat out due to an upper body injury. ... Phoenix was 7-0 when leading after two periods.
Copyright by STATS LLC and The Associated Press
Arena: Wells Fargo Center Location: Philadelphia, Pennsylvania
Referees: Dave Jackson, Dan O'Rourke Linesmen: Greg Devorski, Derek Nansen
Attendance: 19,520 (100.1% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Scott Hartnell (6)
Daniel Carcillo (1)
(Power Play) Unassisted
Martin Hanzal (2)
Assists: Zbynek Michalek, Kevin Porter
Mike Knuble (8)
(Power Play) Assists: Kimmo Timonen, Simon Gagne
Todd Fedoruk (2)
Assists: Martin Hanzal, Mikkel Boedker
Jeff Carter (15)
Assists: Mike Richards, Simon Gagne