Blake Coleman had a goal and an assist, and Andrew Mangiapane, who was also making his preseason debut, had an assist for the Flames. Jacob Markstrom made 21 saves.
Matty Beniers scored his third goal of the preseason, and Martin Jones made 21 saves for the Kraken, who lost for the first time this preseason (4-1-0).
Tanev gave Calgary a 1-0 lead at 7:44 of the first period, scoring from the right circle after his initial shot was blocked by Beniers.
Michael Stone, who is in training camp on a professional tryout contract, extended the lead to 2-0 with a power-play goal at 5:33 of the second period. He has three goals in four preseason games.
Noah Hanifin made it 3-0 at 15:49 with a one-timer from the left point off a pass from Kevin Rooney.
Beniers cut the lead to 3-1 at 2:22 of the third period, converting on a one-timer off a dot-to-dot pass from Alex Wennberg on a power play.
Coleman scored at 9:32 from along the goal line for the 4-1 final.
