The veteran left-winger scored once and also denied a Calgary goal as the Kings wrapped up a perfect four-game road trip with a 4-1 victory over the Flames.
Leading 1-0, the Kings opened up a three-goal cushion early in the second.
A perfect feed from David Jones left TJ Brodie with an empty net late in the second period but the puck was deflected wide after a desperate lunge by Lucic.
''I was joking (it was) my first save of my career,'' said Lucic, who got the shaft of his stick on the puck.
The sequence left Brodie frustrated and his team down 3-0 heading into the third.
''I was just trying to get it on net as quick as I could and unfortunately I didn't get it up enough,'' said Brodie.
Los Angeles goaltender Jonathan Quick appreciated the help.
''That's what we need for success. We need everyone to contribute,'' said Quick. ''You've got to win in different ways. I think we were able to do that this trip.''
Quick, who turned aside 23 shots, picked up all four wins on the road trip, allowing only six goals. He improved to 21-9-1 on the season. Quick is second in wins behind Washington's Braden Holtby (24).
''Obviously he bails us out all the time, so it was nice to bail him out there. If it's 3-1 going into the third period, it could be a completely different game,'' said Lucic.
The goal gave life to the home team as they poured on the pressure after that for an extended stretch.
''They're one of the best teams in the league this year. They came out in the second hungry and got those two goals. That really was the difference,'' said Giordano. ''You can't spot that team three goals.''
The Kings opened up a 12-point lead over the San Jose Sharks in the Pacific Division with the win - their biggest division lead in franchise history.
Calgary (17-18-2) has lost two in a row on home ice after winning a franchise record 11 straight at the Scotiabank Saddledome.
Calgary's power play, ranked 30th in the league, went 0 for 4 while Los Angeles converted on its lone opportunity.
''Possession wise, we had the puck a lot and we were creating. We've got to try to get more pucks to the net,'' said Brodie. ''Those are games where you have to find a way to score on the power play and we didn't.''
Flames goaltender Karri Ramo made 20 saves to fall to 13-12-1.
Notes: Kings center Jeff Carter (lower body) took the game-day skate but did not play, missing his third straight game. ... One line-up change for the Kings saw Christian Ehrhoff return after being scratched for three games. He took the spot of Jamie McBain. ... Calgary's record on New Year's Eve falls to 17-9-3. ... The Flames are last in the NHL on both the power play and the penalty kill.