Mark Giordano, Brendan Morrison and Curtis Glencross also scored as the Flames earned their sixth straight win, their longest streak in two years. Glencross scored an empty-net goal with 6 seconds remaining.
The Flames, who played in Atlanta as an expansion franchise from 1972-80, won in Atlanta for the first time in seven games since leaving the South. Calgary was 0-5-1 in Atlanta since the Thrashers joined the league as an expansion team in 1999.
Bryan Little and Anthony Stewart scored for the struggling Thrashers, who have lost nine of 11.
Miikka Kiprusoff stopped 22 shots as the Flames continued their surge for a playoff spot.
Backlund's go-ahead goal came as he shot through a crowd of players in front of goaltender Ondrej Pavelec in the net after the Thrashers were unable to move the puck out of their zone.
Calgary's previous six-game winning streak was Oct. 21-Nov. 1, 2008.
The Thrashers remained one point ahead of Carolina in the race for the eighth playoff spot in the Eastern Conference. Carolina lost to Toronto 3-0.
Giordano scored immediately after a Flames' power play for a 1-0 lead early in the first period.
Atlanta opened the second period on the attack, tying the game on Little's goal and taking a 2-1 lead midway through the period when Stewart scored on a pass from Evander Kane on a two-on-one rush.
The Flames had a quick answer on Morrison's goal less than a minute later for a 2-2 tie entering the final period.
Notes: The Thrashers placed D Tobias Enstrom on injured reserve with a finger injury before the game. He had missed three straight games. The move is retroactive to Jan. 22. ... Atlanta F Eric Boulton was a healthy scratch for the second straight game. ... Flames LW Niklas Hagman was held out with an undisclosed injury. ... Play was stopped with 2:46 remaining in the second period after Atlanta D Freddy Meyer collapsed at center ice. Meyer skated off the ice with an upper body injury and did not return.