Greiss made 36 saves and Rob Klinkhammer opened the scoring for Phoenix in 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.
Already in dire need of offense, the Flyers lost two proven goal-scorers against Phoenix. Forwards Scott Hartnell (lower body) and Vinny Lecavalier (undisclosed) both left the game with injuries.
And team captain Claude Giroux, a former All-Star who averaged a point per game last season, is without a goal or assist this season.
That was fine with Phoenix.
The Coyotes played the fourth game of a five-game road trip, and have steadied themselves after a brutal start. Greiss stopped all 16 shots in the first period, just the start of a strong effort in his second game of the season.
Klinkhammer scored his first goal of the season only 2:41 into the game when he was the last one to tap the puck past Steve Mason.
Coming off a 33-save effort against the Panthers, Mason was again stout in goal, stopping 29 shots.
He just didn't have enough help on offense.
Adam Hall lost control of the puck and whiffed on a penalty shot against Greiss, dropping the Flyers to 0 for 2 on attempts this season.
Hartnell, another former All-Star without a point this season, left the game in the first with an injury.
The Flyers tied the game 1-all late in the second when Zac Rinaldo whipped the puck off Talbot's right skate and into the net.
That was the last time Rinaldo made a positive contribution for the Flyers. He poked his stick right into Mike Ribeiro's face moments later. With Rinaldo in the penalty box for high sticking, Ekman-Larsson flipped the puck over Mason for the power-play goal with 12.9 seconds left.
Rinaldo was whistled for cross-checking in the third when he nailed Phoenix forward Paul Bissonnette. Bissonnette crashed NFL-style, helmet-to-helmet into Mason. Mason's helmet popped loose and he was down for a few minutes, the team trainer out to check on him. Mason stayed in the game.
The restless crowd booed the Flyers off the ice.