Greiss made 36 saves in his first start of the season.
"How calm did he look in there?'' Coyotes forward
Shane Doan said. ''He was just so calm, relaxed and did a great job."
Rob Klinkhammer opened the scoring for Phoenix in the first. The Coyotes have won two straight games on the road after dropping two straight by a combined 10-2 score. The Coyotes beat the Detroit Red Wings 4-2 Thursday.
"I think I've got to build the trust and show I can play, too," Greiss said.
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.
Already in dire need of offense, the Flyers lost two proven goal-scorers against Phoenix. Flyers general manager Paul Holmgren said forwards Scott Hartnell and Vinny Lecavalier could miss a week after leaving with undisclosed injuries.
"Well it's tougher, but it doesn't matter does it?" Berube asked. "I mean, we've got to win hockey games. People will come in and fill in for them."
Claude Giroux, a former All-Star who averaged a point per game last season, will need to step up. He's without a goal or assist this season. He took four shots on goal and the Flyers attempted a season-high 37 against the Coyotes.
With all those attempts, one goal 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.
''Having a guy come in and really make some good saves at critical times, and build the confidence in the team that you can win in a tough situation, that's exactly what you ask for in a goalie,'' Tippett said.
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
"I'm not sure if it dropped down between my legs or something like that, but I didn't see it," Mason said.
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.
"It's not for a lack of effort because everybody in this room cares tremendously," Mason said, "but we are going to have to start scoring. We need to score more goals and I think the boys can feel that it is going to come. We just have to keep working for it."
NOTES: ''Bones'' star and noted Flyers fan David Boreanaz was at the game. ... The Coyotes finish their road trip Sunday at Carolina. ... Mason dropped to 3-7 lifetime against Phoenix.