Marek Svatos, Milan Hejduk and Ryan Smyth also scored for Colorado, which matched a season high for goals.
Peter Budaj stopped 29 shots, beaten only by Oscar Moller's power-play goal that sneaked under his right arm in the second period.
Jason LaBarbera, who shut out Columbus on Saturday, gave up three goals in the opening 8 minutes, 16 seconds.
It didn't get much better as the Avalanche jumped out to a 6-0 lead midway through the second period.
McLeod had his first two-goal game, scoring his second of the night on a backhanded shot in the second period. He glided into the corner following the goal and lifted his hands in the air, only to be greeted by an agitated Raitis Ivanans of the Kings. The two exchanged shoves before both were sent off to the penalty box for roughing.
McLeod, known more for his grit than goal scoring, had a chance at a hat trick when he found himself on a semi-breakaway early in the third period, but LaBarbera turned back his attempt.
Stewart's first NHL goal came with the Avalanche down a skater. Ian Laperriere gloved the puck out of the zone and Stewart tracked it down, jamming it past LaBarbera. Stewart, who was called up on Friday after Joe Sakic went on injured reserve with a bad back, also had an assist.
Svatos and Hejduk scored 25 seconds apart early in the opening period, igniting the rout.
Sandwiched in between the goals was a fight between Laperriere and John Zeiler, retaliation for a check Zeiler placed on Adam Foote in November.
Zeiler rammed Foote into the boards in that game, a check that drew the Kings right winger a three-game suspension from the league. Foote, who has missed the last nine games with back and knee injuries, just recently returned to skating again.
Laperriere charged after Zeiler, landing a flurry of punches before they were separated. Both drew 5-minute penalties for fighting.
Soon after the fisticuffs ended, Hejduk beat LaBarbera with a shot into the left corner of the net, Hejduk's 12th of the season.
Hejduk is just three goals shy of becoming the fourth player in franchise history to reach 300 goals, joining Sakic (625), Michel Goulet (456) and Peter Stastny (380).
Midway through the opening period, McLeod hit Derek Armstrong into the boards, circled back in front and stuffed the puck into the net.
Armstrong left the game with an upper body injury.
The Avalanche is now 3-0 against the Kings this season.
Notes: Avalanche D Jordan Leopold appeared in his 300th NHL game. ... Smyth obliterated his stick on a first-period slap shot, sending the curved portion 10 rows up into the stands, where it landed in an aisle. ... Svatos left the game in the second period with a back injury. ... Avalanche C Paul Stastny set up Hejduk's goal, giving him 19 assists this season. He now has eight points in the month.