Aliu was recently called up to finish out the season and in the closing contest of the campaign he put two shots past Jonas Hiller.
He opened the scoring 4 minutes into the game and tipped in a shot 7:24 deep in the third period to give the Flames a 4-1 advantage.
Hiller allowed all five goals on 23 shots.
Calgary will miss the playoffs for the third year in a row after reaching the post-season four straight times. Anaheim will miss the playoff chase for the second time in three years.
Celebrity Breakups and divorces of 2014 [PHOTOS]