Clayton Keller tied it 2-2 with a one-timer from the slot off Nick Schmaltz's pass 4:14 into the second period.
"The first period, they were all over us, it was a grind and then after that we got better throughout the game," Coyotes coach Andre Tourigny said. "But the damage was done in this sense they wore us down."
Markstrom was pulled Tuesday with the Flames down 3-1 entering the third period at Dallas on Tuesday. Dan Vladar made five saves to get the win.
"He's our guy. He's going to play lots of games," Sutter said of Markstrom. "It's got nothing to do with [making] him feel good about himself."
Tanev's four points are an NHL career high; he came into the game with 10 points (two goals, eight assists) in 41 games. He had three assists for the Vancouver Canucks against the Avalanche on Jan. 31, 2018.
"If we can round out different ways to win games, and just find other different guys to step up each night and be difference makers, we're going to be a pretty dangerous team down the stretch," Coleman said.
NOTES: The Flames begin a seven-game homestand Feb. 9 against the Vegas Golden Knights. … Lindholm has scored six points (three goals, three assists) in his past six games. … Keller has scored seven points (two goals, five assists) during a six-game point streak. Keller's 17 goals through 45 Arizona games are the most by a Coyotes player since Radim Vrbata (22) in 2011-12. … Calgary had 26 shots in a period Jan. 22, 1986 against New Jersey and on Jan. 2 against Chicago.