The Ducks responded with three goals in a 4:07 span of the third period to cut it to 4-3.
Colangelo, who signed a two-year entry-level contract Thursday after finishing his senior season at Western Michigan University, got to a loose puck behind Wolf and swept it into the net to make it 4-1 at 2:54.
"It felt incredible," Colangelo said. "I kind of blacked out for a second there. I just tried to get a little [celebration] in and just enjoy it with the teammates."
Trevor Zegras made a backhand pass from behind the net to Vatrano, who scored to the short side from below the left circle to make it 4-2 at 6:13.
Zellweger cut it to 4-3 at 7:01 with a wrist shot from above the right circle that nicked two Calgary players before hitting the net.
"Credit to them, they took over the first 10 minutes of the third period," Kadri said. "We needed to settle everybody down."
Kuzmenko scored his second power-play goal of the game to make it 5-3 at 14:22. He scored again from in close at 17:19 and completed the hat trick to make it a 6-3 final.
"As a group, we just battled," Wolf said. "It got to 4-3 with I think 12 minutes left, and we just had to battle. I tried to make a couple saves when I needed to, and we got a couple more (goals), which certainly helped."
Ducks forward Jakob Silfverberg, who earlier in the week announced his retirement from the NHL at the conclusion of the season, played 15:14 in his final game at Honda Center.
"Pretty emotional," said Silfverberg, who played 11 of his 12 NHL seasons in Anaheim. "Obviously it didn't go as planned. The first two periods we were kind of asleep on our part, but we gave it a good push in the third."
NOTES: The Flames went 2-for-5 on the power play and are 12-for-24 in their past eight games. ... Zegras has six points (one goal, five assists) in his past six games. ... Colangelo, who was chosen in the second round (No. 36) of the 2020 NHL Draft, is the seventh Anaheim player to score his first NHL goal this season, the most in the NHL. Zellweger, Jackson LaCombe, Tristan Luneau, Pavel Mintyukov, Urho Vaakanainen and Leo Carlsson are the others.