Moss scored goals 2:23 apart in the second and Calgary held on to snap a four-game losing streak with a 3-2 victory over the Senators on Friday.
"It's been nice so far," said Moss, who had the only three-goal game of his career at Scotiabank Place two years ago. "I've only played here twice, a hat trick and then tonight, so it's been a good feeling."
Sutter used his timeout after Milan Michalek scored with 57.4 seconds left in the third to draw Ottawa within one.
"I think in the third we sat back a little bit," Moss said. "We knew they were going to make a push but we have to be able to weather that better."
The Flames, who had a four-game winning streak prior to their skid, have claimed 12 of a possible 18 standings points in their last nine games. Calgary is 14th overall in the Western Conference, eight points behind Chicago for the eighth and final playoff spot.
"We've just got to stay with it," said coach Brent Sutter, who recently said he wanted his team to get four of every six available points.
"That's one of the goals we have is just making sure that we do that, and take care of our short-term goals and not look at where we're sitting in the standings or what's going on anywhere around us, let's just make sure that we take care of our own business, what we have to do and how we have to play, and the standings will take care of themselves come April."
The Senators, who went 0 for 4 on the power play, are 1-5-2 in their last eight games.
"I thought we played a pretty good game," Michalek said. "We made some mistakes in the second period and that cost us the game. Going into the third we were losing 3-0 so it was hard to come back, but we worked hard and we almost came back."
Brian Elliott, who stopped 23 shots, fell to 0-5-2 in his last seven starts.
Ottawa snapped a six-game skid Thursday night with a 6-4 win in New York over the Islanders as 19-year-old Robin Lehner got the win in his first NHL start.
Karlsson, a 6-foot-5 Swedish rookie, made his eighth start and second straight appearance after relieving Miikka Kiprusoff in Tuesday's shootout loss in Carolina.
"It's a big win for us," Karlsson said. "I think we played really well tonight."
Moss gave Calgary a 1-0 lead with his seventh goal 5:32 into the second. Rene Bourque cut toward the middle from the left side and flipped a backhand pass forward as Moss charged the slot to tip the puck past Elliott.
"I was coming with speed and he kind of saw me coming through the neutral zone and he made a great play," Moss said.
The Flames went ahead 2-0 at 7:55 on Moss' second goal of the game, a wrist shot for his eighth of the season.
Kotalik made it a three-goal lead when he scored with 16.2 seconds left in the second, just four seconds after Ottawa's Chris Neil was tagged with an extra roughing minor for his skirmish with Adam Pardy.
Foligno scored unassisted 9:56 into the third when he snapped a shot past Karlsson for his seventh goal. He got his second point of the game with an assist on Michalek's goal.
- Karlsson has a 3-3-3 mark in 10 games this season.
- Moss got his hat trick in a 6-3 win in Ottawa on Mar. 3, 2009.
- Flames D Robyn Regehr did not play because of a knee injury. D Brendan Mikkelson was inserted into the lineup and played his first game since Dec. 1.
- Ottawa coach Cory Clouston used his timeout after Moss' second goal.