Monahan and Gaudreau both scored once and added two assists. Mark Giordano, Michael Stone and Kris Versteeg, into an empty net, also scored for Calgary (41-27-4). Brian Elliot made 19 saves for his 10th straight win in the Calgary goal.
Anze Kopitar and Nic Dowd replied for the Kings (34-30-7).
The Kings remain six points back of the Nashville Predators in the hunt for the second wild-card berth in the Western Conference. Each team has 11 games remaining.
The Flames are third in the Pacific Division and fifth in the conference, one point ahead of Edmonton Oilers, who host the Kings on Monday.
The Flames chased Kings starting goalie Jonathan Quick with two goals on their first eight shots. Monahan beat him with a wrist shot to the glove side from the left faceoff circle at 8:15 and Stone blasted a slap shot past Quick from almost the identical spot at 11:36.
Kopitar jabbed a short pass from Dustin Brown past Elliott with 1:20 remaining in the first.
Giordano and Gaudreau scored within a minute of each other to open up a 4-1 lead in the second. Giordano's shot from the point hit Alec Martinez's stick and beat Ben Bishop at 47 seconds and Gaudreau scored on a breakaway deke at 1:37, putting a backhander just under the crossbar.
Dowd scored his first goal in 33 games on a tip-in at 5:31, cutting the deficit to 4-2
Calgary held forward Micheal Ferland out of the lineup for fear that he has the mumps. The 24-year-old left winger was placed in isolation earlier Sunday. Ferland has 14 goals and 21 points in 67 games and has been playing on the first line as of late with Monahan and Gaudreau.
NOTES: C Curtis Lazar, who was acquired from the Ottawa Senators at the trading deadline, made his debut for Calgary. The former Senators first-round pick struggled with one assist in 33 games before be shipped west. ... With 622 goals as of Thursday, Kings RW Jarome Iginla is just three goals behind former Colorado star Joe Sakic for 13th on the all-time list. ... The Flames signed their second-round choice from 2016, G Tyler Parsons of Chesterfield, Mich., to a three-year entry contract on Sunday. He plays for the London Knights of the OHL. ... Los Angeles scratches were D Brayden McNabb, C Nick Shore and C Jordan Nolan. ... Calgary's scratches were D Dennis Wideman, C Freddie Hamilton and D Rasmus Anderson.