"Let it be a good lesson for us," Flames coach Brent Sutter said of the Oilers' comeback. "Kipper came up big in the shootout. It's still two points. It's a big win. We know what happened. You just deal with it and get ready and move on for your next one."
Eberle, Kurtis Foster, Magnus Paajarvi and Tom Gilbert scored for Edmonton (2-4-1), which is 0-4-1 in its last five. The Oilers play seven of its next nine games on the road where they're 2-22-3 dating back to mid-December of last season.
Ryan Whitney had two assists to extend his points streak to four games (six assists).
"We were kind of Jekyll-and-Hyde tonight a little bit," Whitney said. "It's got to be more consistent. But that third period shows the kind of team we have."
Trailing 4-1 and being outplayed by a wide margin, Edmonton got a spark when Eberle scored his third goal of the season with 17 seconds left in the second period. Edmonton carried the momentum into the third, when it outshot the Flames 17-10.
"We could have allowed ourselves to be pushed out, and we didn't do that," Oilers coach Tom Renney said. "That's really important. It does take a lot of intestinal fortitude to play in this League in the first place, never mind come from behind."
Edmonton made it 4-3 at 6:52, when Paajarvi took a pass from Andrew Cogliano and bowled his way to the net with the puck deflecting in off the arm of Kiprusoff, who was later screened on the tying goal at 9:19 when Gilbert whipped a shot into the top corner.
"It's a 4-1 game, and you give up a goal with 16 seconds left in the period … you've got to come in and you've got to regroup," Sutter said. "You've got to get back and focus on what we do as a team. I thought we let that bother us to some degree. We got off track there for a bit and got away from what we do."
Morrison opened the scoring via the power play at 5:52 of the first, ripping a slap shot from the blue line past Khabibulin.
Foster tied it less than three minutes later, also on the man advantage, but Bouwmeester's first goal of the season, also on the power play, restored Calgary's lead at 19:40.
Calgary went up 3-1 at 2:02 of the second when Mikael Backlund capitalized on a turnover by Whitney and fed Glencross for his second goal of the season. Morrison gave the Flames a 4-1 lead at 9:48 when he tallied Calgary's League-leading third shorthanded goal on a breakaway.
Edmonton entered the game 9-for-18 on the penalty kill over its previous four games. That statistic became even more glaring when they surrendered goals both times they were shorthanded in the first.
"Special teams … we've got to be better at that and find a way to shut them down," Oilers forward Sam Gagner said. "It was obviously a good feeling to tie it, but it would have been nice to come out with the two points."
Material from wire services and team media was used in this report