Iginla's penalty shot goal in the second period, which tied the game 2-2, made the 33-year-old just the 10th player in NHL history to score 30 goals in 10 or more consecutive seasons.
Mike Gartner and Jaromir Jagr, who accomplished it most recently (1991-92 to 2006-07) top the list at 15 consecutive seasons.
"I never dreamt it would be on a penalty shot," Iginla said. "I've had a few of them in front of the fans here at home and I haven't put any penalty shots in at home until that, so that was a treat for me.
"I definitely feel extremely blessed to hit that and be able to do it 10 years. It's something that when I started out, I never would have dreamt that."
Mark Giordano also scored for Calgary (35-24-9), which moved into sole possession of fifth place in the Western Conference.
Calgary is 15-3-3 in its last 21 games and has been especially hot at the Scotiabank Saddledome, losing just once in regulation in its last 14 games.
Martin Erat and Ryan Suter scored for Nashville (33-24-9), which sit in a three-way tie with Anaheim and Minnesota for ninth place in the West, one point back of the Los Angeles Kings.
Iginla was awarded the penalty shot 59 seconds into the second period when he was tugged from behind by Sergei Kostitsyn as he broke in on Nashville goalie Pekka Rinne. He cut to his right and slid the puck through Rinne's legs to tie the game.
"It's a penalty shot goal that was huge in a 2-1 hockey game and he capitalized on it, and we continued to gain momentum off that," Flames coach Brent Sutter said.
Midway through the third period, Glencross jammed in a rebound off a Rene Bourque shot to put the Flames into the lead.
"We kept trying to get pucks and bodies to the net as much as we could all night," Glencross said. "Olli (Jokinen) tried to put it out front and it was sitting there for me and I had an open net."
Making his 20th straight start, Miikka Kiprusoff made 21 saves to improve to 31-20-5.
Kiprusoff's best stops came in a mad scramble in the game's final seconds as the Predators poured on the pressure with Rinne pulled for an extra attacker. With five seconds left, defenseman Shea Weber bombed a slap shot from the blue line that Kiprusoff sprawled to get a piece of.
Rinne made 33 stops, falling to 0-4-2 in his career versus the Flames, one of only three teams he hasn't beaten. However, he did his best to keep the Predators in there in a second period in which the Flames outshot the visitors 13-4.
With the crowd still buzzing after Iginla's 30th goal, the Calgary veteran sent a perfect pass across to Alex Tanguay on a 2-on-1, but Rinne got a pad out on Tanguay's shot from the slot.
"This was for sure our biggest game of the year, so right now we're disappointed," Rinne said. "But at least we have a chance to bounce back right away in San Jose."
Erat, the most dangerous player on the ice in the first period, opened the scoring at 2:47, knocking in a rebound after Kiprusoff kicked out a pad to deny rookie Jonathon Blum.
"I thought Marty Erat had an exceptional game for us up front," Predators coach Barry Trotz said.
Giordano tied it at 7:15 on the power play on a bizarre goal. The defenseman's shot hit a Predator stick, fluttered into the air, went off Weber, then in off the post.
The Predators regained the lead at 15:58 when Erat sent a pass to Suter, who picked the top corner with from the blue line that went through traffic.
Material from wire services and team media was used in this report.
1 - 0 NSH
1 - 1 Tie
2 - 1 NSH
2 - 2 Tie