Mikko Rantanen had three assists, Nathan MacKinnon had two assists, and Darcy Kuemper made 31 saves for Colorado (16-7-2), which is 5-0-1 in its past six games. The Avalanche scored seven goals in each of their three previous games.
"We can't count on scoring seven goals every game," Kuemper said. "These close, competitive games are a little more fun, especially from my end to play in. That was a really good game of hockey tonight on both sides. It was just a lot of fun to play in."
Joe Thornton and Brandon Montour scored, Carter Verhaeghe had two assists, and Sergei Bobrovsky made 23 saves for Florida (18-5-4), which had a five-game point streak end (4-0-1).
"It's a real fun place to play and they're a real good team, so it was a good little challenge for us," Panthers coach Andrew Brunette said. "I don't think we were particularly sharp with the puck. We managed it fine, and we battled, I just didn't think we were strong enough on the puck in the offensive zone to really sustain a lot of offense."
The Avalanche took a 1-0 lead on Burakovsky's power-play goal with 23 seconds remaining in the second period. Rantanen passed across to Burakovsky at the left hash marks for a shot over Bobrovsky's right shoulder.
Burakovsky made it 2-0 at 2:03 of the third period with a backhand short side from the slot after receiving a pass from Rantanen on the rush.
The Panthers cut it to 2-1 at 7:41 with a power-play goal by Thornton, who converted Verhaeghe's cross-ice pass from the base of the right circle.
The goal was Thornton's 1,534th career point (428 goals, 1,106 assists), moving him past Mark Recchi for 12th in NHL history.
"It's great, but you want to win those games to really celebrate," Thornton said of the milestone. "We pushed hard the last 10 minutes of the third, we really pushed back. We won pretty much every 50-50 battle. It was good desperation hockey and it could have been a good result, it just wasn't."