Phaneuf opened the scoring five minutes into the game. Moss made it 2-0 early in the second and he capped the scoring with four minutes left in the period when he beat Dwayne Roloson to the glove side.
Moss and Dustin Boyd share the team lead with seven points in four games as both try to become regulars this season.
Moss, a Michigan native, has four goals in the preseason, equaling his total in 41 regular-season games last season.
"It gives me a lot of confidence out there," said the Flames' seventh-round draft pick in 2001. "It's still the preseason and you can't read a lot into it. You just have to keep working hard and if you are playing well now hopefully it carries over into the regular season, and you are still helping the team."
Calgary was 8-for-8 in short-handed situations against the Oilers and have not allowed a power-play goal in 29 chances in the preseason.
"We take some pride in that," McElhinney said. "If you are doing well, you are eliminating a lot of chances for the other team. The fact that we haven't allowed one, that's nice to see and hopefully it carries over."
Calgary outshot Edmonton (1-2-0) 31-12 through the first 40 minutes. Devan Dubnyk replaced Roloson for the third period.
"It was a dismal performance," Oilers coach Craig MacTavish said. "But it may not be a bad thing to have at this time of the year as it collectively gives everyone a kick in the rear end. They took it to us in nearly every facet of the game. It's a good motivator for us. Or it better be."
The Oilers claimed defenseman Steve MacIntyre off waivers from the Florida Panthers. The 6-foot-6, 265-pound MacIntyre is in his eighth pro season. He had 213 penalty minutes last season with Providence of the AHL.