The Flames captain completed his first hat trick of the season, and ninth of his NHL career, with a shot from the right circle that got past Kings goalie Jonathan Quick with 4:07 left in the game. It was Iginla's 11th goal in nine games.
He scored Calgary's first goal just 13 seconds after the opening faceoff had tied it 2-2 during a 5-on-3 power play 6:51 into the second.
But after being whistled for tripping early in the third, Iginla was left to nervously watch from the penalty box as the Flames tried to shut down the Kings' power play. Daymond Langkow scored a short-handed goal to break the tie and send Calgary toward victory.
"I was hoping and praying," said Iginla, who was pleased to see the Flames' penalty killers shut down three L.A. power plays on Saturday. The unit allowed four power-play goals to the Blackhawks in a 7-1 loss on Thursday.
"They worked hard all night and were so determined," Iginla said.
David Moss also scored for the Flames, and Miikka Kiprusoff made 23 saves.
"We were assertive, we played an intelligent game, and we were smart," Calgary coach Brent Sutter said. "Iginla played a wail of a game, just not the fact that he scored. He was just rock solid in a lot of areas."
Drew Doughty and Alexander Frolov scored for the Kings, who were in trouble from the first shift.
Iginla gathered a pass from Olli Jokinen at center and whisked a wrist shot just inside the Los Angeles blue line that clipped the skate of Kings defenseman Sean O'Donnell and continued past Quick.
"You always hope for those, they don't happen very often first shift," Iginla said. "I was just trying to use him as a screen, I didn't even see it go in. Scoring that early we were all pretty excited. Especially after a tough last game, to have an early start like that, in an afternoon game, was a big boost."
Frolov, skating on the Kings' top line while versatile forward Ryan Smyth is sidelined with an upper body injury, had gone 10 games without a goal before he swiped in a rebound in the second period to give Los Angeles a 2-1 lead. That came 38 seconds after Doughty tied the game.
"We had a 2-1 lead and they came back and tied it, we had 25 shots maybe, but not too many good scoring chances," Kings captain Dustin Brown said. "That is the result of players not playing hard, and not playing together."
Anze Kopitar, who leads the NHL in scoring, had an assist on Frolov's goal. After averaging more than a point per game in his first 20 games this season, Kopitar has just three assists and no goals in his last five.
"We just needed a few plays to gain some momentum," Kopitar said. "The game was right there for us."
NOTES: Kings D Rob Scuderi plans to skate on his own Sunday morning for the first time since sustaining a lower body injuring at Tampa Bay on Nov. 14. Scuderi hopes to return to the lineup Wednesday at Edmonton. ... The Flames will conclude a two-game road trip at Anaheim on Monday.