Olen Zellweger and Frank Vatrano also scored. Isac Lundestrom, Radko Gudas, Trevor Zegras, Cam Fowler, Jackson LaCombe and Troy Terry posted assists.
John Gibson made 21 saves for Anaheim in his 46th outing of the season.
Tonight's game also marked the final home appearance of longtime Ducks winger Jakob Silfverberg, who Thursday announced his intention to retire from the NHL at the end of the season. Silfverberg skated with Lundestrom and Colangelo, finishing the night with four shot attempts and one blocked shot with a +1 rating.
Andrei Kuzmenko led Calgary offensively with his second career hat trick. Kuzmenko scored five goals in two games against the Ducks with the Flames this season.
Andrew Mangiapane, Nazem Kadri, and Connor Zary also scored for the Flames, who improved to 36-38-5. Rookie goaltender Dustin Wolf, one of five California-born goaltenders in NHL history, earned his sixth career win with 19 stops.
Calgary led 2-0 after the first period, taking the lead on a fortunate early bounce and then adding to it a few minutes later on an impressive individual effort by Kadri.
Mangiapane opened the scoring just under six minutes in as the beneficiary of a bad break for the Ducks, a blocked shot from the slot by Olen Zellweger that kicked right to the Calgary winger alone on the backdoor.
Kadri then doubled the lead just past the midway point of the opening frame, weaving through the Ducks defense on the rush and beating Gibson to the blocker side from the high slot.
The 33-year-old Kadri, who tonight skated in his 900th career NHL game, has scored in three of his last four outings and is now one point shy of his second career 70-point campaign. Kadri found the scoresheet in all three matchups against Anaheim this season.
Kuzmenko then made it 3-0 early in the second period with a power-play goal, pushing the Gibson's leg into the net while the puck lay beneath it. Anaheim challenged the goal for goaltender interference, but it was upheld after review.
Acquired from Vancouver in the February deal that sent veteran center Elias Lindholm to the Canucks, Kuzmenko now has 13 points in his last eight games, including six multi-point efforts. Kuzmenko totaled 21 points in 43 games with Vancouver this season, and already has 21 in 26 appearances as a Flame.
With the secondary helper, defenseman MacKenzie Weegar clinched his third 30-assist season in the last four years.
Zary pushed the visitors' lead to four late in the second with a backhander up over Gibson's glove from in tight.
Down 4-0 heading to the third, Anaheim suddely took control, getting back within a goal in a matter of four minutes.
Colangelo's big moment put the Ducks on the board early in the period, as the youngster crashed the net and found a rebound sitting idly behind Markstrom, quickly punching it home for a goal 22 years in the making.
