Greiss made 36 saves and Rob Klinkhammer opened the scoring for Phoenix at 2:41 of the first.
Max Talbot scored the lone goal for the punchless Flyers, who have only six goals this season and dropped to 1-4. Coach Craig Berube lost his first game after leading the Flyers to a win in his debut. The Flyers' 2-1 win over Florida on Tuesday was their only multiple-goal game this season.
The Coyotes have won two straight games on the road after dropping two straight by a combined 10-2 score.
It is really special. I had a lot of friends and family here tonight, and for my first [NHL] game in here it was great. I played here as an elementary-school player in the city championships and this was my first time back. It was a lot of fun.
— Toronto native Brandon Pirri after scoring 2 goals for Panthers in win at Maple Leafs on Thursday