Blake Coleman, Nazem Kadri, and Yegor Sharangovich scored for the Flames, who won their fourth straight game. Dan Vladař made 25 saves to earn his seventh win of the season.
Durzi opened the scoring at 8:22 of the second period, one-timing a shot from the point past Vladař, and Cooley gave the Coyotes a 2-0 lead at 6:37 of the third period, redirecting Durzi's pass to pot his fourth goal of the season.
Durzi finished the game with a goal, an assist, and a plus-2 rating in 23:05 of ice time.
"He was good," Tourigny said. "He moved the puck well, he made good plays, he was assertive, and he was confident with the puck. A really positive game for him."
The Flames rallied from there, though, as Coleman got Calgary on the board with his 20th goal of the season at 8:54 of the third. Kadri scored 1:03 later to tie it up, beating Ingram from in close.
The game went to overtime, where the Coyotes were called for too many men on the ice with 1:57 remaining, and though they almost killed it off, Sharangovich potted the game-winner with 17 seconds to play in the extra frame.
"We knew what kind of game we were getting coming into it," Durzi said. "Even when we were up two, these circumstances, this time of year, that team, what's on the line, you knew they weren't going to just shut down."
The Coyotes are back in action on Thursday against the Vancouver Canucks to close out their three-game road trip. Puck drop is scheduled for 8 pm MST, and the game will be broadcast on Arizona 61 (TV) and 98.7 FM Arizona Sports (Radio).
