Ribeiro scored his first goal of the contest mid-way through the second period from Mikkel Boedker and former Flame David Moss, and then secored the game winning goal from Keith Yandle just moments after the Flames tied the game at two early in the third period.
With the win, the Coyotes improved to 6-2-2, while the Flames dropped to 4-3-2. The Flames are two points back of the Los Angeles Kings for a playoff spot.
The Flames received goals from Lee Stempniak and Joe Colborne. Colborne, a Calgary native who was acquired by the Flames from the Toronto Maple Leafs on September 28, registered his first goal in a Flames uniform.
Tuesday was also a special night for Flames defenseman Chris Breen, who was playing in his first National Hockey League career game. Breen who was called up to the Flames after the team sent Derek Smith down to Abbotsford on Sunday, had 15 shifts on Tuesday night.
The Flames have also called up Roman Horak from Abbotsford and sent down Blair Jones.
The Flames next play in Dallas on Thursday.
Meanwhile, also according to Sportsnet, members of the Phoenix Coyotes' organization have announced they will be recognized as the Arizona Coyotes starting next season.