The two third-period goals gave the Flames a 4-2 lead and sent them to their first victory of the season.
Columbus was one of the last three teams that opened their season Friday, joining Carolina and the New York Islanders.
The Blue Jackets' Marian Gaborik tied the contest at 2-2 with 4:40 left in the first period and the final stanza ticked past the halfway point with no further scoring.
Hudler, however, put a slap shot over the glove of Sergei Bobrovsky to put the Flames in front with 7:50 remaining. Glencross then took a pass from David Jones that sailed across the crease and also beat the defending Vezina Trophy winner.
The win went to Joey MacDonald, who made 29 saves. Bobrovsky stopped 26-of-30 shots.
Rookie Sean Monahan and T.J. Galiardi scored first-period goals for Calgary, which lost in overtime to Washington in its first game of the year.