Shayne Gostisbehere and Jeff Chychrun each had a goal and an assist for Arizona (7-12-4), which has won just one of its last 10 (1-6-3).
Dan Vladar, starting for the fifth time in the last seven games, made 18 stops to even his record at 4-4-1.
Karel Vejmelka had 24 stops for the Coyotes in falling to 6-7-3.
Down 2-1 to start the third period, Arizona tied it at 5:50 when Chychrun snapped a shot over Vladar's shoulder. It was Chychrun's third goal in seven games since the defenceman returned from a wrist injury that sidelined him the first six weeks of the season.
But nine minutes later, Chychrun took a tripping penalty that proved to be costly.
Calgary regained the lead as Tyler Toffoli neatly set up Kadri, who notched his team-leading ninth goal of the season.
The Flames finished the night a perfect 2-for-3 on the power play, after having been in a slump, going 2-for-21 over the previous seven games.
Arizona went 0-for-2 on the man advantage.
Fuelled by back-to-back power plays early in the first period, Arizona held a 7-1 edge in shots at the 13-minute mark of the first period before Calgary started to tilt the ice in its favour.
After an extended stretch of pressure in the Coyotes' end, Dube opened the scoring deflecting a Chris Tanev point shot at 14:13 of the frame for his fifth goal of the season and fourth goal in his last eight games.
Just under three minutes later, Lindholm netted a power-play marker for his ninth of the campaign.
The Flames piled up 15 shots in a row before the Coyotes, having gone over 15 minutes without testing Vladar, finally directed a puck on the Calgary net seven minutes into the second.
With Vejmelka keeping the visitors within two, Arizona cut its deficit in half at 13:53 of the second. Rookie right-winger Matias Maccelli sent a drop pass to Gostisbehere whose shot found its way through a couple of screens and in off Vladar's arm.
Coyotes defenceman Juuso Valimaki, selected 16th overall in the 2017 draft, is the fourth Flames first-round pick to play against Calgary during its homestand. He follows Matthew Tkachuk (2016) and Sam Bennett (2014) with Florida on Tuesday and Sean Monahan (2013) with the Canadiens on Thursday.
Maccelli's assist extends the 22-year-old's point streak to four games (one goal, five assists). It's also his 15th helper on the season, which leads all rookies. Maccelli is second in rookie scoring behind Seattle's Matty Beniers.
Coyotes: Having not played at home since Nov. 3, Arizona's stretch of 14 straight games on the road concludes on Wednesday in Edmonton.
Flames: Wrap up their five-game homestand on Wednesday against Minnesota.
This report by The Canadian Press was first published Dec. 5, 2022.
Darren Haynes, The Canadian Press