Matthew Tkachuk had a goal, Jacob Markstrom made 40 saves and the Flames improved to an NHL-leading 10-2-2 on the road.
''Sometimes you need your special teams to produce, and the power play was able to get two and the penalty kill did their job again here tonight,'' Lucic said.
Alex Edler got his 100th career goal and Alex Iafallo also scored, but the Kings lost for the seventh time in eight games. Cal Petersen made 29 saves.
''I think it always comes down to little things, the little details in a game, little mistakes here and there,'' Edler said. ''Whether it's getting the puck behind them, turning the puck over here and there. If you do that too many times, eventually you're going to get punched.''
Tkachuk made it 3-1 at 4:54 of the second, with the Flames taking advantage of a turnover in the neutral zone, to get his 11th goal on a wrist shot from the right circle.
Edler got the Kings back to 3-2 with 1:49 left in the period, scoring off the rush to pick up his first goal with Los Angeles after playing 15 seasons in Vancouver.
The Flames used two power-play goals to take a lead into the first intermission after falling behind early.
Lucic scored five-hole to put Calgary in front with 3:32 remaining in the period, getting a goal for the second straight game and giving him three in his past four outings.
The Flames tied it 1-all with 8:41 left. Los Angeles couldn't clear Mikael Backlund's rebound, and he was able to find Mangiapane in the slot for a one-timer. Mangiapane leads Calgary with 16 goals, a league-leading 15 of which have come on the road, and his five power-play goals are tied with Tkachuk for most on the team.
The second power-play unit contributed both goals, and Lucic likes the simple approach they are using.
''Go to the net, pick up loose pucks, find guys off the side of the net, and all that type of stuff. It's worked pretty good for our unit so far, so we need to chip in when we can like we did tonight,'' he said.
Iafallo put the Kings ahead 4:30 into the game, tipping the puck under Markstrom's glove as he had been preparing for a rising shot on Edler's look from the blue line. It was Iafallo's third goal in two games.
''They're not going in offensively, so we've got to almost play perfect defensively. So we're chasing our tail a little bit,'' Los Angeles coach Todd McLellan said.
Darryl Sutter coached against the Kings for the first time since leading them to Stanley Cup championships in 2012 and 2014. Sutter went 225-147-53 in six seasons with Los Angeles before he was fired as part of an organization overhaul following the 2016-17 campaign.
Flames forward Trevor Lewis played against Los Angeles for the first time. Part of those two Cup-winning teams, he had 70 goals and 93 assists in 674 games during his 12 seasons with the Kings.
''It was big to get them the win,'' Tkachuk said. ''They were here for a lot of years and won some championships here and probably have a lot of great memories here, so, sure, this game feels a lot better and is special to them, but it feels better with the win.''
NO PLACE LIKE HOLE
Four of Lucic's seven goals this season have come between the goalie's legs.
''It's a high-percentage shot. If you miss, it's off the pads and it stays alive,'' Lucic said. ''I'd love to tell you how I set it up, but I don't want the goalies to know what my thought process is.''
NOTES: Mangiapane also had an assist on Lucic's goal for his fifth multipoint game. Mangiapane had scored two goals in each of his first four. ... Edler has seven goals and 33 assists in 69 games against Calgary. ... Viktor Arvidsson had two assists in his 400th career game, giving him two goals and four assists during a four-game point streak.
Flames: Visit Anaheim on Friday night.
Kings: Visit Edmonton on Sunday night.
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