" I think that's a good lesson for our group down the stretch here," Giordano said. "There's going to be some downs. There's going to be some ups. That's some pretty good character to show in the third to come back and tie that and then win it."
Dougie Hamilton also scored and Johnny Gaudreau finished with a career-high four assists for the Flames, who move to within one point of Nashville for the first wild card into the Stanley Cup Playoffs from the Western Conference.
"It's a battle. We're in a battle," coach Glen Gulutzan said. "This is what it's like to battle another team that's trying to claw and scrape to be in the playoffs. I thought there was a lot of character shown by both clubs…them coming back and their push in the second and our push-back in the third showed a lot for our group."
Filip Forsberg had a hat-trick and PK Subban and Colin Wilson also scored for the Predators.
Giordano's cross-crease pass to Gaudreau deflected off Forsberg before bouncing by Nashville goaltender Juuse Saros and in to give the Flames their sixth win in the past nine games.
"You can see the respect [Gaudreau] gets out there," Giordano said. "No one really wants to challenge him one-on-one. Try to keep it in his hands. [Sean Monahan] slid up and slid one over to me. That created a 2-on-1 at the net and I'm hoping I get a bounce like that or it gets through to Johnny. I got a lucky bounce."
After giving up a three-goal lead, Calgary pieced together its own rally to come from behind.
Backlund scored his second of the game and 17th of the season with a shot by Saros' blocker to tie the game 5-5 at 10:50 of the third period, and Elliott stopped Calle Jarnkrok at 16:06, and Mike Fisher with 42.9 seconds remaining in regulation to force overtime.
Elliott finished with 23 saves.
"I thought that Ells battled hard," Gulutzan said. "Big saves at the end.
"Johnny had four assists. He made plays tonight. He backchecked. He came back and made some plays and created offence from it. He was fully engaged and he was dangerous.
"[Ferland]. Sam Bennett…loved his game.
"Passion. You saw it in our group. That's what those guys are doing. It's what we've talked about all year is their battle and passion-level they're a great group."
Ferland put the Flames up 1-0 just 46 seconds into the contest when his one-timer off a backhand dish from Gaudreau deflected off Roman Josi and behind Predators starter Pekka Rinne.