Atkinson, a minor-league call-up, scored the shootout winner, and Mason, who was an injury replacement, made 28 saves as the Columbus Blue Jackets won 2-1 on Sunday night.
"It's a nice win," Mason said. "It's not easy coming out to the West Coast. The travel, the time change, it all plays a factor into home-ice advantage out here. To get a win here and get rewarded on the last leg of this trip is nice."
Blue Jackets starting goalie Curtis Sanford, who had beaten Calgary twice this year, left the game with a lower-body injury with 5:23 left in the first period. He appeared to injure his leg while involved in a scramble to the side of the net.
The loss capped a costly weekend for Calgary's pursuit of a playoff spot in the congested Western Conference. Riding a five-game winning streak, the Flames lost 3-1 to the lowly Edmonton Oilers on Friday before getting just one point against the last-place Blue Jackets.
Calgary remained in 11th place in the West, one point behind San Jose and Los Angeles and two back of Phoenix and Colorado, who hold the final two playoff spots.
"Our first was a little bit of a hangover from Edmonton where we weren't quite as sharp or as aggressive, or competed quite as shard, but from the second period on, we played hard," Flames captain Jarome Iginla said. "We competed, we got pucks to the net, we hemmed them in and we need to keep that assertive style going for us. That's how we've got to play and it's the only way we're effective."
The Flames begin a crucial three-game road trip Tuesday night in Colorado.
"Obviously, it's a playoff game, it's a team ahead of us in the standings and as it stands right now, it's a game we have to look like we have to win," Calgary defenseman Mark Giordano said.
With neither team able to score in their first three attempts in the shootout, Atkinson, the Blue Jackets' 22-year-old rookie, scored by faking a shot, then going to his forehand to put the puck past the Flames' Miikka Kiprusoff.
"Obviously, he's a talented player, skilled offensively, and he went in against one of the league's top goalies and really made a tremendous move," Blue Jackets interim head coach Todd Richards said.
Defenseman Nikita Nikitin scored for Columbus, which was playing on back-to-back nights. The Blue Jackets lost 4-3 Saturday night in Vancouver.
Matt Stajan scored for Calgary, whose four-game home winning streak ended.
The Flames were being outshot 5-2 when Sanford was helped off the ice. As soon as Mason settled into the net, the Flames turned on the pressure and carried the play most of the rest of the game, including a 16-3 advantage on shots in the second period.
"We had lots of good scoring chances and we didn't give that many up," Iginla said. "Fortunately, we didn't get it in the shootout and that stings a bit, but the guys played hard."
Calgary tied it 1-1 at 8:34 of the third when Glencross centered a pass to Stajan, whose quick shot went off Mason's shoulder and in.
It was the seventh goal of the season for Stajan, four coming in his last six games.
"I don't think you can say we got outplayed tonight. We almost outshot them by double," Stajan said. "Sometimes we just have trouble finding the back of the net. It's not for lack of effort. We went hard the last two periods and overtime. It's just frustrating right now."
The only goal of the first two periods came from Nikitin at 13:03 of the first. Brett Lebda slid a pass from the blue-line to Nikitin, who one-timed a hard slap shot past Kiprusoff.
Calgary's roster had a different look with veteran Lee Stempniak back after missing 21 games with an ankle injury. However, Tanguay immediately after getting elbowed in the head by Jared Boll in the Blue Jackets zone 6:31 into the second period. He did not return for the third.
It seemed to spark the Flames, who showed more emotion and greater urgency after that.
"In the second period, I don't think they got out of their end for more than two minutes," Iginla said. "Some days, it doesn't go your way, but we keep our heads up, we get ready for Colorado and we play them and we can tie them and keep going."
- Columbus wins the season series over the Flames 3-0-1.
- Calgary has lost its last four shootouts and falls to 3-8 on the season. Columbus improves to 4-5 in shootouts.
- Five of Nikitin's 23 points have come against Calgary (two goals, three assists) this season. He was the points leader for both teams in the four-game season series.
- Stajan played in his 600th career game.