That's five goals in the last three games for the 24-year-old left wing, who on this night took advantage of a promotion to Colorado's top line and a chance to skate with Nathan MacKinnon and Joonas Donskoi.
MacKinnon assisted on both of Burakovsky's goals to give him 13 points (five goals, eight assists) in his last six games.
Vladislav Kamenev also scored for Colorado (13-6-2), which has won five of six. The Avalanche are 3-1-0 on a five-game road trip that wraps up Thursday in Minnesota.
Philipp Grubauer got the win in his first game back after missing five with a lower-body injury. He had 31 stops to improve to 7-3-2.
David Rittich made 23 saves for the Flames and fell to 9-6-3.
The Avalanche opened the scoring 3:21 in when Burakovsky took a cross-ice pass from MacKinnon and fired a shot just inside the post.
Before the first period was over, Burakovsky made it 2-0 at 18:45 with his 10th of the season. Off a faceoff win by MacKinnon in the Flames end, the Swede got the puck along the sideboards, cut back sharply to get some separation from defenseman Rasmus Andersson and ripped a shot under the crossbar.
The 2-0 lead for the Avs came despite being outshot 13-7.
After Kamenev, set up by J.T. Compher on a 2-on-1, made it 3-0 at 13:15, the Flames got on the board at 17:41 of the second when Ryan beat Grubauer under the crossbar.
The goal ended Calgary's scoreless streak at 167 minutes, 44 seconds, dating back to the third period against Dallas last Wednesday. The Flames were shut out in both games on their weekend trip to Arizona and Vegas.
Calgary drew within one on Mangiapane's fourth goal at 15:44 of the third, setting up a furious finish. But despite getting a power play for the last 21 seconds and pulling their goalie, the Flames couldn't take advantage of the 6-on-4.
Colorado LW Matt Calvert (head) sat out. He had been playing alongside MacKinnon. ... With Travis Hamonic (lower body) out, Brandon Davidson made his debut on the Flames blue line. ... Also playing in his first game for Calgary was Zac Rinaldo, just up from Stockton (AHL). The Flames are his fifth NHL team.
Avalanche: At the Minnesota Wild on Thursday night.
Flames: At the Stanley Cup champion St. Louis Blues on Thursday night.