Matt Coronato scored the go-ahead goal midway through the third period, and Nazem Kadri had a goal and an assist for the Flames (14-17-4), who had lost two of three after winning three straight. Dustin Wolf made 21 saves.
Chandler Stephenson and Kaapo Kakko scored for the Kraken (12-14-6), who have lost four straight games and have gone 1-9-1 in their previous 11.
Kadri tied it 2-2 on the power play at 10:04 of the third period after he one-timed a pass from Andersson past Daccord.
Coronato scored 1:15 later to give Calgary a 3-2 lead at 11:19. He took a pass from Andersson before lifting a shot from the left circle to the top corner over Daccord’s glove.
Jonathan Huberdeau recorded the secondary assist for his 800th NHL point.
Backlund scored into an empty net at 19:52 for the 4-2 final.
After a scoreless first period in which the Flames outshot the Kraken 18-6, Stephenson gave the Kraken a 1-0 lead at 7:52 of the second period.
While cutting towards the net through the left circle, Stephenson took a pass from Eeli Tolvanen on his backhand before tucking a forehand shot just inside the far post by the outstretched left leg of Wolf.
Backlund tied it 1-1 at 10:20 when he drove hard to the net before a shot by Andersson deflected off his skate and past Daccord. It was the 200th assist of Andersson’s NHL career.
Kakko’s power-play goal put the Kraken ahead 2-1 at 17:16, redirecting a pass from Ryker Evans.