Nathan MacKinnon had a goal for the Avalanche, who are 10-2-2 over their last 14 games. Semyon Varlamov was pulled midway through the second period after allowing five goals on 23 shots.
Philipp Grubauer replaced Varlamov and gave up two goals on 15 shots.
"I don't think there's any positive you could take out of this game," Grubauer said. "We made it easy for them, the best team in the league."
Tampa Bay held the high-scoring line of MacKinnon, Mikko Rantanen and Gabriel Landeskog to three points. The trio entered with 48 goals and 124 points.
"We weren't giving them time and space at all," Lightning coach Jon Cooper said. "When you don't give them any space, especially the big line, it can be frustrating."
Rantanen got his NHL-leading 48th point with an assist that extended his points streak to 11 games (14 assists, 19 points).
Stamkos opened the scoring from the left circle off a pass through the slot by Nikita Kucherov during a power play 3:05 into the game. Kucherov has 21 assists and 26 points over his last 13 games.
"I thought it started with the PP," Johnson said. "Getting that quick goal, I think we just kept rolling with that."
After Stamkos scored on a breakaway backhander at 13:15 of the first, MacKinnon made it 2-1 just 59 seconds later.
MacKinnon has 20 goals in 30 games, which ties Joe Sakic's Colorado team record, set in 1995-96, for the fewest games needed to reach the mark.
Johnson put Tampa Bay up 3-1 late in the first.
Stamkos made a pass from the left circle while falling down to Yanni Gourde, who then set up Killorn's goal two minutes into the second that put Tampa Bay ahead 4-1.
Palat and Cirelli added second-period goals.
"We need to be a lot better than we were tonight," Colorado center Tyson Jost said. "Everybody knows that."
Palat had a power-play goal in the third.
NOTES: Stamkos has 67 multi-goal games. ... Injured Tampa Bay G Andrei Vasilevskiy (fractured left foot) and D Anton Stralman (upper body) both took part in the morning skate. Vasilevskiy could return within the next three weeks while Stralman's status is being reviewed on a weekly basis. ... Rantanen, Landeskog and MacKinnon have a point on the same goal the 17 times. ... Colorado C Vladislav Kamenev left in the first with an undisclosed injury.
UP NEXT
Avalanche: Return home Tuesday night to play Edmonton.
Lightning: Host the New York Rangers Monday night.
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