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.
There's not much to say. We played like [garbage]. I think every guy in the room should be completely embarrassed about how they played tonight. Every single person. To start a road trip, one of the biggest road trips and have a division rival chasing you down and have a ton on the line, it's ridiculous how we played tonight.
— Anaheim forward Andrew Cogliano after the Ducks' 7-2 loss to the Flames on Wednesday