Iginla got his 27th and 28th goals - the 401st and 402nd of his career - and Peters scored for his first career point as the Flames beat Alex Auld three times in the first period to build a 3-2 lead.
"We're very happy for them," said Iginla, who recorded his milestone goal in Sunday's 8-6 loss to Tampa Bay. "First of all, Warren Peters' goal, not only to see him get his first but to see him get such a big goal, it was a big emotional lift for our team when we'd been up and they had some momentum. I thought from there we started to get a lot more energy."
Moss scored on one of Calgary's two shots in the second period and added his second goal of the game on a power play early in the third. He got his hat trick into an empty net with 16.3 seconds remaining as the Flames kicked off a season-high seven-game trip with their fifth straight road win.
"To see him get his first hat trick was very exciting," Iginla said. "He's worked so hard and he's going to the net, he's a big part of our power play, which is improving, and it's good to see it pay off and nice to see him get his trick."
Miikka Kiprusoff stopped 22 shots for Calgary, which improved to 8-1-2 since a season-high four-game losing streak.
"It wasn't my best game, for sure," Kiprusoff said. "It was a tough start, but after that I was able to play a little bit better. The guys played a strong game and it was nice to take these two points."
Auld, who stopped 11 of 15 shots, fell ill and left after the second period. Brian Elliott made six saves in the third.
Senators center Jason Spezza got 17 minutes in penalties for instigating a fight with Dion Phaneuf 1:37 into the third after the Flames defenseman dropped Dany Heatley with an open-ice shoulder check.
"I hit him with one - he told me I did - and I just tried to hang on," said Spezza, much better known for his playmaking than his pugilism. "The quick reaction when you see your guy down is you want to help."
Phaneuf had little problem with Spezza's reaction.
"I felt it was a clean hit but obviously they took exception," Phaneuf said. "It's part of the game. Hits are still part of the game and fights are still part of the game, so you guys will make a big deal about it, but it's part of the game."
Heatley, who hadn't seen a replay of the hit, appreciated his teammate's intervention.
"I guess the issue is whether it will be an elbow or not, but obviously I didn't see him coming or otherwise I wouldn't have got hit. So I don't know if he hit me with the shoulder or the elbow," Heatley said. "Spezza's a good teammate and to jump in like that shows a lot of character,"
Moss, who made it 4-2 when he beat Auld for his 17th goal 4:57 into the middle period, scored his 18th goal against Elliott on the ensuing power play to increase Calgary's lead to 5-2.
Iginla's first-period goals put the Flames up 1-0 and 3-2. He opened the scoring 2:18 in and restored Calgary's one-goal lead with the fifth goal of the opening period.
Flames right wing David Van der Gulik also got his first career point when he set up Peters' goal that tied it at 2. Peters took Van der Gulik's pass to the left of the Senators' goal and spun around before putting a shot from a sharp angle past Auld, who somehow was beaten on the play despite hugging the left post.
Ottawa enjoyed a brief lead after Kuba tied it with his second goal of the season on a power play and Fisher got his 10th goal to make it 2-1.
Foligno scored his 11th goal with 5:02 remaining.
Notes: Kiprusoff improved to 5-0 in six career appearances against Ottawa, including a 6-3 win in Calgary on Dec. 27. ... Peters and Van der Gulik each appeared in their third game overall. Peters, who played one game earlier this season, played his second game since he was recalled from Quad City on Saturday. Van der Gulik played his third straight game since he was called up on Feb. 26.