Backlund snapped a 2-2 tie by putting a wrist shot past Ondrej Pavelec with 5:57 remaining in the third. Glencross scored into an empty net with 6 seconds remaining.
Calgary extended its winning streak to a season-high six games.
The Thrashers overcame a 1-0 deficit after the first period to take a 2-1 lead on goals by Bryan Little and Anthony Stewart. Brendan Morrison tied it for Calgary with 7:51 to play in the second.
Miikka Kiprusoff picked up win with 22 saves.
Pavelec stopped 20 shots while the Thrashers were losing their third straight. Atlanta has scored more than two goals just once in its last nine games.
Celebrity Families of 2014 [PHOTOS]