Mangiapane gave the Flames a 1-0 lead at 1:54 of the first period when he chipped a loose puck on a blocked shot by Korpisalo's blocker on the power play.
Rasmus Andersson thought he scored a short-handed goal at 7:39 for Calgary, but Los Angeles successfully challenged that Noah Hanifin preceded the puck into the offensive zone.
Durzi tied it 1-1 at 9:24 with a shot top corner over Markstrom's blocker from the top of the right face-off circle.
Duehr put the Flames up 2-1 at 17:59 when he corralled a rebound off the end boards from Trevor Lewis' wide chance and shot short side before Korpisalo could get set.
"I think he was just trying to shoot," Duehr said. "Just a good bounce there for us and I was able to put it in."
Markstrom made a right-pad save on Kevin Fiala's clear-cut breakaway from center ice with 33 second remaining in the first.
"It's huge. He was good all night," Calgary center Elias Lindholm said. "Real sharp. We need him to play like that."
The Flames thought they scored again at 11:49 of the second period, but there was no conclusive evidence in a video review initiated by the NHL Situation Room to determine that the puck completely crossed the goal line.
"On our behalf there wasn't a lot of [offensive] zone time, yet we had some really good scoring chances, long chances that had us looking at Markstrom and he made some really good saves," Kings coach Todd McLellan said. "At the other end, we spent too much time in our end, and I thought our game management for the first time in a long time was poor."
Markstrom scrambled to his left to make an arm save on Fiala on a backdoor pass from Mikey Anderson from the left point at 14:41.
He also stopped Kopitar's tip with 41 seconds remaining to preserve the win.
"We got some quality looks," Kopitar said. "Got to give credit to their goaltender. He played pretty well. That's what happens this time of the year. You're going to get their team's best, especially that team. Obviously, they're pretty desperate in the position they're in. It is what it is."
NOTES: Korpisalo lost for the first time in regulation in six starts with the Kings. He went 4-0-1 after he was acquired with defenseman Vladislav Gavrikov from the Columbus Blue Jackets on March 1. ... Kings forward Viktor Arvidsson had a three-game goal and point streak end (seven points; five goals, two assists) ... Flames forward Matt Coronato, selected with the No. 13 pick in the 2021 NHL Draft, signed his entry-level contract Sunday but did not play. ... Kings forward Gabriel Vilardi did not travel with them to open their four-game road trip because of an upper-body injury.