Lance Bouma scored twice during Calgary's four-goal third period and the Flames rallied to beat the Oilers 4-2 at Scotiabank Saddledome.
"Obviously, we have come from behind in the past so we know we can do it and we have the belief in here," Bouma said. "That's huge for us. We always say going into the third period that the third is always our best and we always seem to find a way.
"I think the biggest thing is just confidence. We have the belief in here that going into the third period, whether we're down by two or down by three, that we can come back in a game. Our conditioning is great. We just have that belief and we find a way."
Paul Byron and Sean Monahan also scored and Jonas Hiller made 17 saves for Calgary (27-20-3), which has an NHL-leading nine wins when trailing after two periods. The Flames also have an NHL-best 63 third-period goals while allowing the fewest in the League (32).
Calgary owns the second Western Conference wild-card position for the Stanley Cup Playoffs and increased its lead on the Los Angeles Kings to three points, though the Kings have a game in hand. The Flames moved within three points of the Winnipeg Jets for the first wild-card spot and have a game in hand.
"It was simple mistakes," Eberle said of the Oilers' failure to close out the game. "We shot ourselves in the foot tonight. We turned a couple pucks over and I mean, it's just been kind of the same case. Every guy in the room has done it. Myself, a lot of guys. It seems like every night there's a couple plays that shoot us and that's where we lost. We've known the way we needed to play to win this game and we just didn't do it in the third."
The Flames trailed 2-0 after 40 minutes but needed less than half the third period to turn the deficit into a lead.
Byron finally solved Oilers goaltender Ben Scrivens at 2:56. Mason Raymond circled the Oilers' net, popped out the other side and sent a shot through a screen that Byron tipped past Scrivens to cut the Oilers' lead to 2-1. It snapped a 28-game goal-scoring drought for Byron and a span of 105:28 without a goal for Calgary.
"It's kind of funny how those bounces go," Byron said. "You get so many breakaways and great chances to score and you just get a fluky goal where you're just standing in the right place and it hits your shaft and goes in. That's kind of the luck of the game."
The Flames needed less than 3 1/2 minutes to pull even.
After failing to bunt a puck out of midair into an open net behind Scrivens earlier in the shift, Bouma collected a pass from Mikael Backlund that missed David Jones and beat the Oilers goaltender at 6:16 to tie the game at 2-2.
"The puck was finding me that shift," Bouma said. "The one just kind of bounced over my stick there and an open net there too. I just stuck with it and [Backlund] made a great play, Jones made a great play before that and it found the back of the net."
Bouma added his second of the night with 3:33 remaining. Backlund forced a neutral-zone turnover, broke into the Edmonton zone and fed Bouma, who lifted his eighth of the season over Scrivens' glove to give Calgary a two-goal lead and cap the comeback.
Bouma had a chance to complete the hat trick in the final seconds with the Edmonton net empty but couldn't find the handle.
"I missed a couple open nets there," Bouma said. "Oh well, that's the way it goes. I'm happy with the two but I want to get more for sure."
It took the Oilers 2:43 from the start of the game to jump ahead.
Off the ensuing faceoff following an icing, Ryan Nugent-Hopkins won the draw back to Eberle in the slot; he corralled the puck and fired his 13th of the season past Hiller's blocker to give Edmonton a 1-0 lead.
"[Nugent-Hopkins] just made a great second effort play and I just threw it on net," Eberle said. "We had a good screen."
The Oilers made it 2-0 at 11:41 when Eberle picked up the puck to the left of Hiller and circled behind the net before spotting Pouliot on the other side. He caught Hiller out of position and scored his 11th of the season.
The Flames held a 6-5 advantage in shots in a scoreless second period, but their best chance came without a Scrivens save.
David Wolf, a late addition for his first NHL game in place of the ill Jiri Hudler, came close to pulling the Flames back within one near the midway point of the second period but hit the crossbar behind the Oilers goaltender.
Wolf left the game early in the third period and did not return after sustaining a lower-body injury.
"It was a little bit disappointing but you know what, with a win in my first NHL game nothing can ruin my day, even a little injury like that," Wolf said. "I'm really proud to play the game and proud the guys bounced back in the third period and won the game."